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!