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

Positive rate of change from a graph

Maths

In this unit, pupils saw that an arithmetic sequence can be represented graphically and that this is a linear relationship. Any point on the line satisfies this relationship. In the future unit, pupils learn how to find a value that satisfies the relationship when the second value is known, without the aid of the graph.

The sequences unit allowed pupils to explore different ways of generating sequences and then representing an arithmetic sequence graphically. This served as an introduction to this unit on graphical representations of linear equations.

Graphical representations of linear equations

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

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

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

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

Which of these best describes the gradient?

Which of these lines have a positive gradient?

Match the lines labelled A, B, C, D with the correct gradient.

The coordinate (0,0) can also be called the {{ }}.

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

What is the missing number in this table of values for the equation $$y=5x-3$$ ?

A drink is made from 3 litres of juice and 9 litres of soda. Use the ratio table to work out the amount of soda needed for 1 litre of juice.

What is the missing value in this ratio table?

For every change of +1 in $$x$$ there is a change of -3 in $$y$$

For every change of +1 in $$x$$ there is a change of +3 in $$y$$

For every change of +1 in $$y$$ there is a change of -3 in $$x$$

For every change of +2 in $$x$$ there is a change of -5 in $$y$$

For every change of +3 in $$x$$ there is a change of -9 in $$y$$

A table of values is shown for the relationship $$y = 11 - 3x$$. Which of these is true for this relationship?

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

Positive rate of change from a graph

Lesson outcome

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