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

We call this the multiplier when exchanging currency, for example.

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

Answer

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.

You can look back at this introduction at any point by clicking on the red help button on the screen.