PR.6A, SEC 1, drct prpn y=kx (50)

Question 1 of 51

1. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧮 The variables $k$ and $l$ are directly proportional.

If $k = 5$ when $l = 1$ ,

find $k$ when $l = 6$ .
- k =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 2 of 51

2. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📏 The variables $v$ and $w$ are directly proportional.

If $v = 9$ when $w = 3$ ,

calculate $v$ when $w = 10$ .
- v =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 3 of 51

3. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🚀 The variables $t$ and $u$ are directly proportional.

If $t = 16$ when $u = 4$ ,

calculate $t$ when $u = 6$ .
- t =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 4 of 51

4. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📐 The variables $u$ and $v$ are directly proportional.

If $u = 8$ when $v = 2$ ,

calculate $u$ when $v = 11$ .
- u =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 5 of 51

5. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧠 The variables $k$ and $l$ are directly proportional.

If $k = 18$ when $l = 2$ ,

find $k$ when $l = 7$ .
- k =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 6 of 51

6. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔬 The variables $s$ and $r$ are directly proportional.

If $s = 28$ when $r = 7$ ,

find $s$ when $r = 2$ .
- s =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 7 of 51

7. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🖇️ The variables $c$ and $d$ are directly proportional.

If $c = 15$ when $d = 3$ ,

determine $c$ when $d = 4$ .
- c =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 8 of 51

8. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔗 The variables $x$ and $y$ are directly proportional.

If $x = 25$ when $y = 5$ ,

determine $x$ when $y = 3$ .
- x =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 9 of 51

9. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📝 The variables $y$ and $x$ are directly proportional.

If $y = 11$ when $x = 1$ ,

determine $y$ when $x = 5$ .
- y =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 10 of 51

10. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📏 The variables $p$ and $q$ are directly proportional.

If $p = 14$ when $q = 7$ ,

find $p$ when $q = 12$ .
- p =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 11 of 51

11. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📝 The variables $g$ and $h$ are directly proportional.

If $g = 6$ when $h = 12$ ,

calculate $g$ when $h = 30$ .
- g =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 12 of 51

12. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🏆 The variables $n$ and $p$ are directly proportional.

If $n = 27$ when $p = 9$ ,

calculate $n$ when $p = 4$ .
- n =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 13 of 51

13. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🪄 The variables $x$ and $y$ are directly proportional.

If $x = 18$ when $y = 6$ ,

calculate $x$ when $y = 2$ .
- x =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 14 of 51

14. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🏆 The variables $s$ and $t$ are directly proportional.

If $s = 49$ when $t = 7$ ,

find $s$ when $t = 9$ .
- s =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 15 of 51

15. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📊 The variables $q$ and $r$ are directly proportional.

If $q = 18$ when $r = 3$ ,

find $q$ when $r = 10$ .
- q =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 16 of 51

16. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🚀 The variables $g$ and $h$ are directly proportional.

If $g = 16$ when $h = 4$ ,

determine $g$ when $h = 9$ .
- g =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 17 of 51

17. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔄 The variables $p$ and $q$ are directly proportional.

If $p = 10$ when $q = 2$ ,

find $p$ when $q = 6$ .
- p =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 18 of 51

18. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧠 The variables $d$ and $e$ are directly proportional.

If $d = 20$ when $e = 4$ ,

calculate $d$ when $e = 9$ .
- d =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 19 of 51

19. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📚 The variables $w$ and $z$ are directly proportional.

If $w = 21$ when $z = 7$ ,

calculate $w$ when $z = 5$ .
- w =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 20 of 51

20. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📊 The variables $r$ and $s$ are directly proportional.

If $r = 8$ when $s = 4$ ,

calculate $r$ when $s = 9$ .
- r =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 21 of 51

21. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🪄 The variables $h$ and $i$ are directly proportional.

If $h = 13$ when $i = 1$ ,

determine $h$ when $i = 3$ .
- h =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 22 of 51

22. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📚 The variables $w$ and $z$ are directly proportional.

If $w = 21$ when $z = 7$ ,

calculate $w$ when $z = 5$ .
- w =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 23 of 51

23. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📈 The variables $x$ and $y$ are directly proportional.

If $x = 12$ when $y = 3$ ,

determine $x$ when $y = 5$ .
- x =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 24 of 51

24. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📈 The variables $j$ and $k$ are directly proportional.

If $j = 32$ when $k = 8$ ,

find $j$ when $k = 5$ .
- j =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 25 of 51

25. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧠 The variables $n$ and $m$ are directly proportional.

If $n = 27$ when $m = 9$ ,

determine $n$ when $m = 1$ .
- n =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 26 of 51

26. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧮 The variables $m$ and $n$ are directly proportional.

If $m = 6$ when $n = 1$ ,

find $m$ when $n = 9$ .
- m =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 27 of 51

27. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔗 The variables $l$ and $m$ are directly proportional.

If $l = 6$ when $m = 2$ ,

calculate $l$ when $m = 11$ .
- l =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 28 of 51

28. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔎 The variables $f$ and $e$ are directly proportional.

If $f = 8$ when $e = 2$ ,

find $f$ when $e = 5$ .
- f =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 29 of 51

29. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🌀 The variables $u$ and $v$ are directly proportional.

If $u = 15$ when $v = 3$ ,

calculate $u$ when $v = 8$ .
- u =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 30 of 51

30. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

💡 The variables $o$ and $p$ are directly proportional.

If $o = 40$ when $p = 5$ ,

determine $o$ when $p = 2$ .
- o =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 31 of 51

31. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🎯 The variables $d$ and $c$ are directly proportional.

If $d = 24$ when $c = 6$ ,

calculate $d$ when $c = 3$ .
- d =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 32 of 51

32. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📐 The variables $a$ and $b$ are directly proportional.

If $a = 21$ when $b = 3$ ,

determine $a$ when $b = 5$ .
- a =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 33 of 51

33. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🛠️ The variables $r$ and $t$ are directly proportional.

If $r = 18$ when $t = 9$ ,

find $r$ when $t = 3$ .
- r =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 34 of 51

34. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📈 The variables $x$ and $y$ are directly proportional.

If $x = 50$ when $y = 10$ ,

calculate the value of $x$ when $y = 30$ .
- x =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 35 of 51

35. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

💡 The variables $r$ and $t$ are directly proportional.

If $r = 11$ when $t = 1$ ,

determine $r$ when $t = 4$ .
- r =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 36 of 51

36. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📏 The variables $c$ and $d$ are directly proportional.

If $c = 18$ when $d = 6$ ,

calculate $c$ when $d = 11$ .
- c =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 37 of 51

37. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📐 The variables $v$ and $w$ are directly proportional.

If $v = 22$ when $w = 2$ ,

calculate $v$ when $w = 7$ .
- v =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 38 of 51

38. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧮 The variables $p$ and $q$ are directly proportional.

If $p = 12$ when $q = 4$ ,

determine the value of $p$ when $q = 15$ .
- p =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 39 of 51

39. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🛠️ The variables $h$ and $j$ are directly proportional.

If $h = 30$ when $j = 5$ ,

calculate $h$ when $j = 2$ .
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 40 of 51

40. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🖇️ The variables $e$ and $f$ are directly proportional.

If $e = 9$ when $f = 3$ ,

find $e$ when $f = 4$ .
- e =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 41 of 51

41. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🖇️ The variables $z$ and $a$ are directly proportional.

If $z = 30$ when $a = 6$ ,

find $z$ when $a = 10$ .
- z =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 42 of 51

42. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📈 The variables $m$ and $n$ are directly proportional.

If $m = 9$ when $n = 3$ ,

calculate $m$ when $n = 7$ .
- m =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 43 of 51

43. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🛠️ The variables $h$ and $j$ are directly proportional.

If $h = 30$ when $j = 5$ ,

calculate $h$ when $j = 2$ .
- h =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 44 of 51

44. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔢 The variables $g$ and $h$ are directly proportional.

If $g = 14$ when $h = 7$ ,

determine $g$ when $h = 2$ .
- g =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 45 of 51

45. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔎 The variables $b$ and $c$ are directly proportional.

If $b = 7$ when $c = 1$ ,

determine $b$ when $c = 8$ .
- b =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 46 of 51

46. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📈 The variables $m$ and $n$ are directly proportional.

If $m = 9$ when $n = 3$ ,

calculate $m$ when $n = 7$ .
- m =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 47 of 51

47. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧮 The variables $a$ and $k$ are directly proportional.

If $a = 7$ when $k = 1$ ,

find $a$ when $k = 10$ .
- a =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 48 of 51

48. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🎯 The variables $k$ and $l$ are directly proportional.

If $k = 5$ when $l = 1$ ,

calculate $k$ when $l = 7$ .
- k =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 49 of 51

49. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔢 The variables $a$ and $b$ are directly proportional.

If $a = 12$ when $b = 4$ ,

determine $a$ when $b = 9$ .
- a =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 50 of 51

50. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📐 The variables $p$ and $s$ are directly proportional.

If $p = 5$ when $s = 5$ ,

determine $p$ when $s = 12$ .
- p =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.
Question 51 of 51

51. Question
Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📚 The variables $w$ and $z$ are directly proportional.

If $w = 24$ when $z = 8$ ,

find $w$ when $z = 3$ .
- w =
  
  ⌨️ Enter your answer for x in the field provided.
Correct

Incorrect
Hint

💡 Direct proportion: turn y = kx into a number machine.

When a question says “directly proportional”, use y = kx.

You might also see “y is proportional to x” or the symbol y ∝ x, which means there exists a constant multiplier k so that y = kx.

It is good practice to rewrite this as a number machine, because maths is all about inputs and outputs.

Treat x as the input and y as the output, and note that the expression on the left of the equals sign is usually the output.
```
x  ──▶  [ × k ]  ──▶  y
```
To find what k is, you must be given one pair of values for x and y at the same point.

Compute k = output ÷ input = y ÷ x.

Once you know k, you can find any y from any x by running the machine using y = kx.

You can also find any x from any y by reversing the machine using x = y ÷ k.

Remember: going x → y multiply by k, and going y → x divide by k.

Draw the machine each time to keep the direction clear.

PR.6A, SEC 1, drct prpn y=kx (50)

PR.6A, SEC 1, drct prpn y=kx (50)

Quiz Summary

Information

Results

Results

Categories

1. Question

Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧮 The variables k and l are directly proportional.

If k=5 when l=1,

find k when l=6.

k =

⌨️ Enter your answer for x in the field provided.

Hint

2. Question

Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📏 The variables v and w are directly proportional.

If v=9 when w=3,

calculate v when w=10.

v =

⌨️ Enter your answer for x in the field provided.

Hint

3. Question

Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🚀 The variables t and u are directly proportional.

If t=16 when u=4,

calculate t when u=6.

t =

⌨️ Enter your answer for x in the field provided.

Hint

4. Question

Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

📐 The variables u and v are directly proportional.

If u=8 when v=2,

calculate u when v=11.

u =

⌨️ Enter your answer for x in the field provided.

Hint

5. Question

Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🧠 The variables k and l are directly proportional.

If k=18 when l=2,

find k when l=7.

k =

⌨️ Enter your answer for x in the field provided.

Hint

6. Question

Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔬 The variables s and r are directly proportional.

If s=28 when r=7,

find s when r=2.

s =

⌨️ Enter your answer for x in the field provided.

Hint

7. Question

Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🖇️ The variables c and d are directly proportional.

If c=15 when d=3,

determine c when d=4.

c =

⌨️ Enter your answer for x in the field provided.

Hint

8. Question

Topic: Direct Proportion.

Please have pen and paper handy to show workings out. 📝

🔗 The variables x and y are directly proportional.

If x=25 when y=5,

determine x when y=3.

x =

⌨️ Enter your answer for x in the field provided.

Hint

9. Question

🧮 The variables $k$ and $l$ are directly proportional.

If $k = 5$ when $l = 1$ ,

find $k$ when $l = 6$ .

`k =`

📏 The variables $v$ and $w$ are directly proportional.

If $v = 9$ when $w = 3$ ,

calculate $v$ when $w = 10$ .

`v =`

🚀 The variables $t$ and $u$ are directly proportional.

If $t = 16$ when $u = 4$ ,

calculate $t$ when $u = 6$ .

`t =`

📐 The variables $u$ and $v$ are directly proportional.

If $u = 8$ when $v = 2$ ,

calculate $u$ when $v = 11$ .

`u =`

🧠 The variables $k$ and $l$ are directly proportional.

If $k = 18$ when $l = 2$ ,

find $k$ when $l = 7$ .

`k =`

🔬 The variables $s$ and $r$ are directly proportional.

If $s = 28$ when $r = 7$ ,

find $s$ when $r = 2$ .

`s =`

🖇️ The variables $c$ and $d$ are directly proportional.

If $c = 15$ when $d = 3$ ,

determine $c$ when $d = 4$ .

`c =`

🔗 The variables $x$ and $y$ are directly proportional.

If $x = 25$ when $y = 5$ ,

determine $x$ when $y = 3$ .

`x =`

📝 The variables $y$ and $x$ are directly proportional.

If $y = 11$ when $x = 1$ ,

determine $y$ when $x = 5$ .

`y =`

📏 The variables $p$ and $q$ are directly proportional.

If $p = 14$ when $q = 7$ ,

find $p$ when $q = 12$ .

`p =`

📝 The variables $g$ and $h$ are directly proportional.

If $g = 6$ when $h = 12$ ,

calculate $g$ when $h = 30$ .

`g =`

🏆 The variables $n$ and $p$ are directly proportional.

If $n = 27$ when $p = 9$ ,

calculate $n$ when $p = 4$ .

`n =`

🪄 The variables $x$ and $y$ are directly proportional.

If $x = 18$ when $y = 6$ ,

calculate $x$ when $y = 2$ .

`x =`

🏆 The variables $s$ and $t$ are directly proportional.

If $s = 49$ when $t = 7$ ,

find $s$ when $t = 9$ .

`s =`

📊 The variables $q$ and $r$ are directly proportional.

If $q = 18$ when $r = 3$ ,

find $q$ when $r = 10$ .

`q =`

🚀 The variables $g$ and $h$ are directly proportional.

If $g = 16$ when $h = 4$ ,

determine $g$ when $h = 9$ .

`g =`