Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other.

Two variables are in direct proportion if they have a constant multiplicative relationship.

Problem solving with direct and inverse proportion

Maths

In the linear graphs unit, pupils learnt to recognise and interpret graphs that illustrate direct and inverse proportion. In this unit, pupils learn how to represent these relationships algebraically.

Direct and inverse proportion

Two variables are inversely proportional if there is a constant {{}} relationship between one variable and the reciprocal of the other. 

When $$y\propto \sqrt{x}$$, when $$x$$, increases by 96%, what proportion does $$y$$ increase by?

Given the following proportions, select which are the correct proportional relationships when : 
$$a \propto c$$, $$c \propto b$$, $$b \propto \frac{1}{e}$$ and $$a \propto \frac{1}{f}$$.

When $$y \propto x$$ and $$x \propto z^2$$, when $$y=75$$, $$x=3$$ and when $$x=128$$, $$z=4$$. Write $$y$$ in terms of $$z$$.

When $$y\propto x^2$$, when $$x$$ increases by 20%, what proportion does $$y$$ increase by?

Two variables are in {{}} proportion if they have a constant multiplicative relationship. 

Which graph shows no proportional relationship?

$$y \propto x^2$$, when $$y=192$$, $$x=4$$. Work out the value of $$y$$ when $$x=10$$.

Which of these graphs show $$y \propto \frac{1}{x^n}$$? 

$$y \propto \sqrt{x}$$, when $$y=40$$, $$x=4$$. Work out the value of $$y$$ when $$x=100$$.

$$y \propto \frac{1}{x^2}$$, when $$y=9.6$$, $$x=5$$. Work out the value of $$y$$ when $$x=10$$. Give your answer as a decimal. 

This lesson will be removed by end of Summer Term 2025.

Problem solving with direct and inverse proportion

Lesson outcome

This lesson will be removed by end of Summer Term 2025.