# Understand Direction Proportion

In this worksheet, students will be asked to resolve problems related to direct proportion.

Key stage:  KS 3

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Solve Problems Involving Direct and Inverse Proportion

Difficulty level:

### QUESTION 1 of 10

Direct proportion refers to the relationship between two variables where their ratio is equal to a constant value.

Example:

Given that y is directly proportional to x and that x = 19 when y = 133.

Find:
(i) a formula connecting y and x
(ii) the value of y when x = 13
(iii) the value of x when y = 119

y ∝ x

So, y = kx for a constant k.

(i) Given x = 19, when y = 133,

133 = k x 19

k = 133 ÷ 19 = 7

Therefore, the formula is y = 7x

(ii) When x = 13, y = 7 x 13 = 91

(iii) When y = 119, x = 119 ÷ 7 = 17

It's useful to have paper and a pencil in order to record your own workings.

These are not the kind of questions you can calculate mentally.

Over to you!

Given that y is directly proportional to x and that x = 8 when y = 192.

Find a formula connecting y and x.

24

12

192

8

Given that y is directly proportional to x and that x = 8 when y = 192.

Find the value of y when x = 15.

24

12

192

8

Given that y is directly proportional to x and that x = 8 when y = 192.

Find the value of x when y = 600.

24

12

192

8

Given that y is directly proportional to x and that x = 7 when y = 105.

Find a formula connecting y and x.

y = 7x

y = 105x

y = 15x

y = x

Given that y is directly proportional to x and that x = 7 when y = 105.

Find the value of y when x = 9.

y = 7x

y = 105x

y = 15x

y = x

Given that y is directly proportional to x and that x = 7 when y = 105.

Find the value of x when y = 75.

x = 15

x = 0.5

x = 7

x = 5

Given that y is directly proportional to x and that x = 19 when y = 133.

Find a formula connecting y and x.

y = 7x

y = 19x

y = 133x

y = 26x

Given that y is directly proportional to x and that x = 19 when y = 133.

Find the value of y when x = 13.

y = 7x

y = 19x

y = 133x

y = 26x

Given that y is directly proportional to x and that x = 19 when y = 133.

Find the value of x when y = 119.

x = 17

x = 119

x = 7

x = y

Given that y is directly proportional to x and that x = 12 when y = 192.

Find a formula connecting y and x.

x = 17

x = 119

x = 7

x = y

• Question 1

Given that y is directly proportional to x and that x = 8 when y = 192.

Find a formula connecting y and x.

24
EDDIE SAYS
y ∝ x y = kx k = y/x = 192/8 = 24 y = 24x How did you do?
• Question 2

Given that y is directly proportional to x and that x = 8 when y = 192.

Find the value of y when x = 15.

EDDIE SAYS
y = 24x y = 24 × 15 = 360 Strong start maths-whiz, how are you finding applying the method? If you get stuck you can always refer back to the introduction.
• Question 3

Given that y is directly proportional to x and that x = 8 when y = 192.

Find the value of x when y = 600.

EDDIE SAYS
y = 24x x= y/24 = 600/24 x = 25
• Question 4

Given that y is directly proportional to x and that x = 7 when y = 105.

Find a formula connecting y and x.

y = 15x
EDDIE SAYS
y ∝ x y = kx k = y/x = 105/7 = 15 y = 15x This one was trickier, so don't sweat it if you got caught out!
• Question 5

Given that y is directly proportional to x and that x = 7 when y = 105.

Find the value of y when x = 9.

EDDIE SAYS
y = 15x y = 15 × 9 y = 135 Did you working out match what I've written above?
• Question 6

Given that y is directly proportional to x and that x = 7 when y = 105.

Find the value of x when y = 75.

x = 5
EDDIE SAYS
y = 15x x = y/15 = 75/15 x = 5 Take a deep breath, you've got this and you're now halfway!
• Question 7

Given that y is directly proportional to x and that x = 19 when y = 133.

Find a formula connecting y and x.

y = 7x
EDDIE SAYS
y ∝ x y = kx k = y/x = 133/19 = 7 y = 7x This is great work, one final push!
• Question 8

Given that y is directly proportional to x and that x = 19 when y = 133.

Find the value of y when x = 13.

EDDIE SAYS
y = 7x y = 7 × 13 y = 91
• Question 9

Given that y is directly proportional to x and that x = 19 when y = 133.

Find the value of x when y = 119.

x = 17
EDDIE SAYS
y = 7x x = y/7 = 119/7 x = 17 By now you should be feeling super confident!
• Question 10

Given that y is directly proportional to x and that x = 12 when y = 192.

Find a formula connecting y and x.

EDDIE SAYS
y ∝ x y = kx k = y/x = 192/12 = 16 y = 16x Great focus, that's another activity ticked off!