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

The absolute value of a number is its distance from zero.

Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

Negative 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

Which of these graphs have a negative gradient?

Match the graphs to the correct gradient.

Starting with the steepest, put these gradients in order of steepness.

Which lines would be parallel to the one shown if drawn on the same axes?

rate of change in $$x$$ direction with respect to positive $$y$$ direction

rate of change in $$x$$ direction with respect to negative $$y$$ direction

rate of change in $$y$$ direction with respect to negative $$x$$ direction

rate of change in $$y$$ direction with respect to positive $$x$$ direction

Which of these is the correct explanation for how gradient is calculated?

Which of these tables of values show a relationship which will have a positive gradient when plotted?

Which is the correct ratio table for this graph?

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

Negative rate of change from a graph

Lesson outcome

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