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Understand Direct Proportion

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

Worksheet Overview

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



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


(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


A simpler way to do this is to set it out as a ratio:



Divide both sides by 19 to find the value when x is 1:

1: 133 ÷ 19 


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!

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