GCSE-readyReal-life graphs and rates of change
Graphs show how one quantity changes with another: money in different currencies, a journey, or water filling a bath.
Conversion graphs
Read across from one axis to the line, then down (or up) to the other axis.
If £10 = €12, then £35 = 3.5 × €12 = €42.
Distance-time graphs
A horizontal line means stopped. A steeper line means faster.
Speed = distance ÷ time, which is the gradient of the line.
This journey goes 40 km in the first hour, stops for half an hour, then travels 60 km in 1.5 hours.
| Time (hours) | 0 | 1 | 1.5 | 3 |
|---|---|---|---|---|
| Distance from home (km) | 0 | 40 | 40 | 100 |
Rates of change
The gradient of each section is a rate of change, with units: km per hour, litres per minute, pounds per month.
Rate = change in the up quantity ÷ change in the across quantity.
Using the journey table, find the speed in the last section.
- Distance: 100 − 40 = 60 km
- Time: 3 − 1.5 = 1.5 hours
- Speed = 60 ÷ 1.5
Answer: 40 km/h
Conversion graphs for quantities in direct proportion are straight lines through the origin. On a distance-time graph, flat means stopped and steeper means faster. The gradient is the rate of change.
- Direct proportion
- Two quantities where one is always the same multiple of the other: if one doubles, so does the other. y = kx.
- Origin
- The point (0, 0) where the x-axis and y-axis cross.
- Gradient
- The steepness of a line: change in y ÷ change in x. In y = mx + c it is m.
- Time
- 60 seconds = 1 minute, 60 minutes = 1 hour. 0.5 hours = 30 minutes, 0.25 hours = 15 minutes.
- Speed
- Distance travelled per unit of time. Speed = distance ÷ time, for example in km/h or m/s.
- Not “The object is moving at constant speed”. Constant speed is a sloping straight line.
Try two quick questions
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2 more questions
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A journey table shows time (hours) 0, 2, 2.5, 4 and distance from home (km) 0, 90, 90, 150. What is the speed in the first section?
Show the answer
Answer: 45 km/h
90 km in 2 hours: 90 ÷ 2 = 45 km/h.
A journey table shows time (hours) 0, 1, 1.75, 3 and distance from home (km) 0, 50, 50, 110. For how many minutes did the traveller stop?
Show the answer
Answer: 45 minutes
The distance stays at 50 km from 1 to 1.75 hours: 0.75 hours = 45 minutes.
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Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.