These sometimes come up on the exam – so don’t forget about them!

**Direct Proportion**

If two quantities are in direct proportion then when one increases or decreases the other increases or decreases by the same percentage.

On a graph this is shown with a straight line through the origin: y = kx

**Inverse Proportion**

As one quantity increases the other one decreases.

The equation and graph for this is y = k/x

**Other Proportions**

Proportional to can be shown by the symbol .

Examiners might throw in some nasty looking proportions so here’s some examples of what you might expect.

y is proportional to x squared -> y x²

y is proportional to x cubed -> y x³

y is proportional to the square root of x -> y √x

y is inversely proportional to x cubed -> y 1/x³

In an exam you will probably need to change the proportion into an equation to work something out. To do so just change the proportional sign to an =k – here’s some examples to show you what we mean

y x² becomes y = kx²

y x³ becomes y = kx³

y √x becomes y = k√x

y 1/x³ becomes y = k/x³

**So What Sort Of Question Will I Be Asked On This Topic?**

Let’s take an example!

**Example:** y is inversely proportional to x. When x = 12, y = 3. Find the constant proportionality and find x when y = 8.

*First write down the proportionality. Here it is inverse proportion so*

y 1/x

*Replace the sign with an =k*

y = k/x

*You can then manipulate the equation like normal*

So xy = k

*Put in the values from the question*

3 x 12 = 36

So k = 36

So the constant proportionality is 36…so now you can find x when y = 8

8x = 36

so x = 4.5