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 vertical and horizontal 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 are coordinates of points on the line $$y = 5$$?

Which of these are coordinates of points on the line $$x = -3$$?

all lines can be written in the form $$y = mx + c$$

The equations of which type of lines cannot be written in the form $$y = mx + c$$?

There is a solution to the equation $$-{2\over 3}x + 6 = 8$$ when $$x =$${{}}. Use the graph to help you.

The gradient of the line with equation $$y = 3x -4$$ is {{ }}.

What is the gradient of the line with equation $$y = 5 - 100x$$?

Which of these are coordinates of points on the $$x$$-axis?

Which of these are coordinates of points on the $$y$$-axis?

Which of these coordinates are on the line with equation $$y = 2x + 1$$?

Which of these coordinates are on the line with equation $$y = 7 - x$$?

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

Checking and securing understanding of drawing vertical and horizontal graphs

Lesson outcome

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