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

Finding the constant of proportionality for directly proportional relationships

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

Abstract inverse proportion

Finding the constant of proportionality for 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

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.

Finding the constant of proportionality for directly proportional relationships

Lesson outcome