The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

The gradient is a measure of how steep a line is.

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

Checking and securing understanding of drawing linear graphs

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

Which of these is the $$x$$-intercept of the line $$2x + 3y = 6$$?

Which of these is the $$y$$-intercept of the line $$2x + 3y = 6$$?

Which of these coordinates are on the line with equation $$y = 10-3x$$?

Which of these is the correct graph for the line with equation $$2x + y = 8$$? Each square represents 1 unit on each axis.

Match each equation of a line to its key features. 

The gradient of the line with equation $$2y = 4x -6$$ is {{ }}.

Match each point to its correct coordinates.

In algebra, when you replace variables with values you call this ...

This is a table of values for a linear equation, but there is an error. Which value is the error?

You are given the linear equation $$y=3x +4$$. When $$x=2$$, $$y$$ is {{ }}.

You are given the linear rule $$y= 5 - 2x $$. When $$x=-4$$, $$y$$ is {{ }}.

Which of these could represent an $$x$$-intercept?

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

Checking and securing understanding of drawing linear graphs

Lesson outcome

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