Using graphs is not just about reading off values. In real-life contexts, the intercept, gradient and area underneath the graph can have important meanings such as a fixed charge, speed or distance.

The concepts of gradient and rate of change are explored

All real-life graphs can be used to estimate or read-off values.The actual meaning of the values will depend on the labels and units shown on each axis. Sometimes:

the gradient of the line or curve has a particular meaning

the -intercept (where the graph crosses the vertical axis) has a particular meaning

the area under the graph has a particular meaning

Example:

This graph shows the cost of petrol.

It shows that 20 litres will cost £23 or £15 will buy 13 litres.

Gradient = or

Using the points (0, 0) and (20, 23), the gradient = = 1.15.

The units of the axes help give the gradient a meaning.

The calculation was:

The gradient shows the cost per litre. Petrol costs £1.15 per litre.

The graph crosses the vertical axis at (0, 0). This is known as the intercept.

It shows that if you buy 0 litres, it will cost £0.

Example:

This graph shows the cost of hiring a ladder for various numbers of days.

Using the points (1, 10) and (9, 34), the or .

The units of the axes help give the gradient a meaning.

The calculation was:

The gradient shows the cost per day. It costs £3 per day to hire the ladder.

The graph crosses the vertical axis at (0, 7).

There is an additional cost of £7 on top of the £3 per day (this might be a delivery charge for example).