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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

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.

Over to you!

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