Real-life linear graphs
Objective. Interpret straight-line sections in contextual graphs.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A real-life linear graph shows how a quantity changes steadily over time or distance, where straight sections represent constant rates such as fixed speed or cost. The gradient of each straight section gives the rate during that interval, and a flat section means no change is happening. On a distance–time graph, a steep straight line rising means fast steady travel, while a horizontal section means the object has stopped. Always read the axes labels and units before interpreting the steepness of any section.
Worked example
A real-life graph shows a taxi fare starting at £3 and rising by £2 per mile. Find the fare for a 6-mile journey using the linear graph's equation.
- 1Write the equation from the graph: fare = 2m + 3
- 2Substitute m = 6: fare = 2(6) + 3
- 3Multiply first: 2 × 6 = 12
- 4Add 3: 12 + 3 = 15, so the fare is £15
Answer: £15
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Practice
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Start practisingCommon mistake. Pupils often think a flat section on a distance–time graph means the object has returned to the start, when it actually means it has stopped moving. Always check whether distance is increasing, constant, or decreasing before describing motion.
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