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Using and interpreting graphs - AQAReal-life graphs

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.

Part of MathsAlgebra

Real-life graphs

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 \(y\)-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 拢23 or 拢15 will buy 13 litres.

A graph showing the cost of petrol. The y axis shows cost in pounds from zero to 30 and the X axis shows litres from zero to 24. The graph shows that 20 litres will cost 拢23 or 拢15 will buy 13 litres.

Gradient = \(\frac{\text{change up}}{\text{change right}}\) or \(\frac{\text{change in y}}{\text{change in x}}\)

Using the points (0, 0) and (20, 23), the gradient = \(\frac{23}{20}\) = 1.15.

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

The calculation was: \(\frac{change~in~y}{change~in~x} = \frac{change~in~cost}{change~in~litres} = \frac{change~in~拢}{change~in~l} = 拢/l.\)

The gradient shows the cost per litre. Petrol costs 拢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 拢0.

Example:

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

A graph showing the cost of ladder hire. The y axis is cost in pounds from zero to 40 and the X axis shows time in days from zero to 10. The gradient shows that it costs 拢3 per day to hire the ladder.

Using the points (1, 10) and (9, 34), the \(gradient = \frac{change~up}{change~right}\) or \(\frac{change~in~y}{change~in~x} = \frac{34-10}{9-1} = \frac{24}{8} = 3\).

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

The calculation was: \(\frac{\text{change in y}}{\text{change in x}} = \frac{\text{change in cost}}{\text{change in days}} = \frac{\text{change in 拢}}{\text{change in days}}= 拢/day\)

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

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

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

Next page
Distance-time and displacement-time graphs

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