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. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.

Problem solving with real-life graphs

Maths

The work on gradient in the prior unit is expanded further in this 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.

Real-life graphs

This graph shows __________ rate of change between speed and time.

Which speed-time graph matches this distance-time graph?

Which distance-time graph matches this speed-time graph?

Match these descriptions to the graph of this car journey.

Which moment represents the longest stop on this displacement-time graph?

A linear graph like this shows __________ between $$x$$ and $$y$$.

A constant rate of change on a distance-time graph shows __________.

This distance-time graph shows the journey of a cyclist. When were they travelling fastest?

This distance-time graph shows the journey of a cyclist. When did the cyclist stop?

A horizontal line on this graph represents __________.

This speed-time graph shows the journey of a car. When is it travelling fastest?

Starter Quiz