Direct and inverse proportion

Direct proporation

If two quantities are in direct proportion, as one increases, the other increases by the same percentage. If y is directly proportional to x, this can be written as y ∝ x

Graphs and proportion

If y is proportional to a power of x, we can draw a graph that shows the relationship. The shape of the graph will depend on the power and the constant of proportionality.

Inverse proportion

Inverse proportion is when one value increases as the other value decreases.

A simple example of two things that are in the same proportion is the amount of apples you might buy and the amount you pay for them. If you buy twice as many apples as your friend, you pay twice as much.

We can write the connection between the cost and the amount as an equation: Cost of apples = price per apple × number of apples bought. This can also be written as y = kx, where k is the cost (the price per apple).

Direct proportion to powers

y can be directly proportional to x2 , x3 and other powers of x. They can always form an equation with k, a constant multiplier (the constant of proportionality), at the start.