Just when you have are hopefully getting to grips with **direct proportion using algebra**, this activity will throw inverse proportion at you too!

**Key Information:**

Two quantities are said to be **inversely proportional** if, as one quantity increases, the other quantity decreases at the same rate.

They are doing the opposite to each other.

For example, the faster you run over a given distance, the less time it takes.

When two variables are **proportional** (so one increases as the other does, or vice versa), we would write this as: y ∝ x

We use the letter k to represent the constant, and we would find the multiplier using the formula: y = k × x

However, for **inverse proportion**, the opposite is happening, so we have to rearrange our formula to become:

y ∝ k/x

It's time to practise now...

**e.g. x is inversely proportional to y, and when x = 4 then y = 9.**

**a) Find y when x = 2.**

Firstly, we need to find our multiplier by adding in the numbers we know:

y ∝ k/x

9 = k ÷ 4

k = 9 × 4

So k = 36

Now we can substitute this value into our formula with the new value for x:

y = 36 ÷ 2

y = 18

So when x = 2, y = 18.

**b) Find x when y = 3.**

All we need to do here is to take the same multiplier and divide by the value given for y:

3 = 36 ÷ x

3x = 36

x = 12

Okay - let's dive in!

In this activity, you will find the values of unknown variables which are inversely proportional to each other, using appropriate notation to express these relationships algebraically.