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.

Proportion modelled algebraically

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

Problem solving with direct and inverse proportion

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

Which of the following show an inversely proportional relationship between $$y$$ and $$x^n$$?

Which of these graphs show direct proportion between $$y$$ and $$x^n$$?

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

Match the value of $$k$$ with the relevant graph for $$y=\frac{k}{x}$$

Match the value of $$k$$ with the relevant graph for $$y=\frac{k}{x^2}$$

Which of the following equations of a line show the direct proportion between $$x$$ and $$y$$?

Which of the following equations of a curve show the direct proportion between $$x^2$$ and $$y$$?

Which of the following show that $$x$$ is inversely proportional to $$y$$?

 Given that $$y$$ is directly proportional to $$𝑥$$ and $$𝑦=30$$ when $$x=5$$, write the equation connecting $$y$$ and $$x$$.

Given that $$y$$ is directly proportional to $$𝑥^2$$ and $$𝑦=4375$$ when $$x=25$$, write the equation connecting $$y$$ and $$x^2$$.

 Given that $$y\propto \frac{1}{𝑥}$$ and $$𝑦=4$$ when $$x=50$$, write the equation connecting $$y$$ and $$x$$.

Starter Quiz

Which of the following equations of a line show the direct proportion between $$x$$ and $$y$$?