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

Finding the constant of proportionality for directly proportional relationships

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

Which of the following equations represent $$y$$ being directly proportional to $$x$$ or a power of $$x$$ in some way?

Match each equation to its correct value of $$k$$.

$$a$$ is directly proportional to $${b}^3$$

$$a$$ is directly proportional to $${\sqrt[3]{b}}$$

$$a$$ is directly proportional to $${\sqrt{b}}$$

$$a$$ is directly proportional to $${b}^2$$

$$y$$ is directly proportional to $$x^2$$.  When $$x$$ = 6, $$y$$ = 108.  Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 11.

$$y$$ is directly proportional to $${\sqrt[3]{x}}$$.  When $$x$$ = 64, $$y$$ = 20.  Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 343.

$$y$$ is directly proportional to $${\sqrt[3]{x}}$$.  When $$x$$ = 64, $$y$$ = 20.  Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$x$$ when $$y$$ = 25.

What letter is used to represent the constant of proportionality?

Which of the following equations represent $$y$$ being directly proportional to some form of $$x$$?

$$y$$ is directly proportional to $$x$$.  When $$x$$ = 70, $$y$$ = 245.  Write an equation connecting $$x$$ and $$y$$.

$$y$$ is directly proportional to $$x$$.  When $$x$$ = 8, $$y$$ = 13.2.  Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 35.

$$y$$ is directly proportional to $$x$$.  When $$x$$ = 8, $$y$$ = 13.2.  Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$x$$ when $$y$$ = 66.

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

Finding the constant of proportionality for directly proportional relationships

Lesson outcome

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