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

Finding the constant of proportionality for direct proportion

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

the additive relationship between $$x$$ and $$y$$

When dealing with equations of direct proportion we use the equation $$y = kx$$.  What does $$k$$ represent? 

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

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

$$y$$ is directly proportional to $$x$$.  When $$x$$ = 13, $$y$$ = 52.  Write an equation connecting $$x$$ and $$y$$.

$$y$$ is directly proportional to $$x$$.  When $$x$$ = 6, $$y$$ = 13.2.  Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$y$$ when $$x$$ = 14.

$$y$$ is directly proportional to $$x$$.  When $$x$$ = 6, $$y$$ = 13.2.  Write an equation connecting $$x$$ and $$y$$ and use this to find the value of $$x$$ when $$y$$ = 123.2.

Any non-zero number multiplied by its {{ }} is equal to 1.

Which of the following tables show direct proportion? 

The time taken to make 10 000 items and the number of machines

The height of a staircase and the number of stairs

The cost to wallpaper a room and the size of the room

The number of sweets in a bag and the number of people sharing it

Decide which of the following would share a directly proportional relationship.

$$h$$ is directly proportional to $$g$$.  When $$g$$ = 17, $$h$$ = 93.5.  Find $$h$$ when $$g$$ = 25.

$$h$$ is directly proportional to $$g$$.  When $$h$$ = 17, $$g$$ = 93.5.  Find $$g$$ when $$h$$ = 60.5.

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

Finding the constant of proportionality for direct proportion

Lesson outcome

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