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

Finding the constant of proportionality for 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

Proportion modelled algebraically

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

Match the constant of proportionality for each of the following inverse proportions.

$$y$$ is inversely proportional to $$x^2$$

Match the correct proportionality statement with an example equation.

$$y$$ is $$\propto \frac{1}{x}$$. When $$y$$ = 4, $$x = 2$$. What is the equation to show the inversely proportional relationship between $$x$$ and $$y$$?

$$y$$ is $$\propto \frac{1}{x}$$. When $$y=\frac{1}{5}$$, $$x=2$$. Work out $$y$$ when $$x=10$$. Give your answer as a decimal.

$$y$$ is $$\propto \frac{1}{x^2}$$. When $$y=\frac{1}{6}$$, $$x=2$$. Work out $$y$$ when $$x=\sqrt{8}$$.

$$y$$ is $$\propto \frac{1}{\sqrt{x}}$$. When $$y=2.4$$, $$x=100$$. Work out $$y$$ when $$x=64$$.

Match the statement with the correct notation.

Match the coordinates with the directly proportional equations.

$$y$$ is proportional to $$x$$. When $$y$$ = 48, $$x$$ = 12. What is the equation to show the direct proportion between $$x$$ and $$y$$?


$$y$$ is proportional to $$x$$. When $$y$$ = 20, $$x$$ = 80. What is the equation to show the direct proportion between $$x$$ and $$y$$?

$$y$$ is proportional to $$x^2$$.
When $$y$$ = 200, $$x$$ = 10.
What is the equation to show the direct proportion between $$x$$ and $$y$$?

$$y$$ is proportional to $$\sqrt{x}$$.
When $$y$$ = 2, $$x$$ = 36.
What is the equation to show the direct proportion between $$x$$ and $$y$$?

Finding the constant of proportionality for inverse proportion

Lesson outcome