Real-life graphs

Real-life graphs represent practical situations such as distance-time, conversion graphs and water-filling graphs. You need to read, interpret and sometimes draw these graphs.

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Key facts to remember

1On a distance-time graph, the gradient = speed. A flat line means stationary.
2On a speed-time graph, the gradient = acceleration, and the area under the graph = distance.
3Conversion graphs are straight lines through (or near) the origin.
4The y-intercept and gradient of a real-life graph both have practical meanings.
5A steeper gradient means a greater rate of change.

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Worked examples

Example 1

A distance-time graph shows a journey: 0 to 30 min covers 15 km, then stationary for 10 min, then returns 15 km in 20 min. Find the speed for the first section.

Working

Speed = distance ÷ time
Distance = 15 km, Time = 30 min = 0.5 hours
Speed = 15 ÷ 0.5 = 30 km/h

Answer30 km/h

Example 2

A graph converts pounds (£) to euros (€). It passes through (0, 0) and (50, 58). Use it to convert £120 to euros.

Working

Gradient (exchange rate) = 58 ÷ 50 = 1.16 euros per pound
£120 × 1.16 = €139.20

Answer€139.20

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Common mistakes

✗On a distance-time graph, misreading a horizontal section as movement rather than rest.

✗Confusing distance-time and speed-time graphs — on speed-time, area = distance.

✗Ignoring units — check whether time is in minutes or hours before calculating speed.

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Exam tips

✓Always read axis labels and scales carefully before interpreting a graph.

✓For distance-time graphs, the gradient (rise ÷ run) gives speed — include units in your answer.

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