The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.

An intercept is the coordinate where a line or curve meets a given axis.

Checking and securing understanding of finding the equation of the line from the graph

Maths

The work on gradient in this unit is expanded further in the future unit by considering gradient as the rate of change and interpreting this in context. The gradient of the tangent is introduced as a way of estimating the gradient of a curve.

In the prior unit, pupils drew a linear graph from its equation and related the features of the graph to its equation. In this unit, pupils consider equations that produce parallel or perpendicular graphs and how their equations relate to each other.

Linear graphs

How much the $$x$$ values change for every 1 increase in $$y$$

How much the $$y$$ values change for every 1 increase in $$x$$

How much the $$x$$ values change for every 1 decrease in $$y$$

How much the $$y$$ values change for every 1 decrease in $$x$$

Which of these descriptions best describes the gradient?

What is the step on the $$y$$ axis of this graph?

A jug of drink is made from 6 cups of juice and 18 cups of soda. Use the ratio table to work out the amount of soda needed for 1 cup of juice.

What is the missing value in this ratio table?

For every change of +1 in $$x$$ there is a change of -4 in $$y$$

For every change of +1 in $$x$$ there is a change of +4 in $$y$$

For every change of +1 in $$y$$ there is a change of -4 in $$x$$

For every change of +5 in $$x$$ there is a change of -20 in $$y$$

For every change of +12 in $$y$$ there is a change of +3 in $$x$$

A table of values is shown for the relationship $$y = 12 - 4x$$. Which of these is true for this relationship?

the multiplier of a specified variable in a term

the point where a line crosses a specified axis

a relationship which, when plotted, forms a straight line

Match each equation of a line to its key features. 

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

Checking and securing understanding of finding the equation of the line from the graph

Lesson outcome

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