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

Checking and securing understanding of direct proportion graphs

Checking and securing understanding of inverse proportion graphs

Abstract direct proportion

Finding the constant of proportionality for direct proportion

Finding the constant of proportionality for directly proportional relationships

Abstract inverse proportion

Finding the constant of proportionality for inverse proportion

Proportion modelled algebraically

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.

In this unit, pupils learn how to represent direct and inverse proportion algebraically as an extension of work done in the linear graphs unit.

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. 

Starter Quiz

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