On a distance-time graph, the gradient of the line is the speed. Time is on the horizontal axis and distance from the start is on the vertical axis.
This appears in travel questions where you must find speeds, a stop, or an average speed from a graph. It builds on converting speed units.
How do you read the graph step by step?
- Check the axes and scales. Note the units (km and hours, or m and seconds) and the value of each small square.
- Split the graph into straight segments. Each straight segment has its own speed.
- For each segment, find the change. Change in distance ÷ change in time = speed.
- Interpret each shape. A sloping line up is moving away, a horizontal line is stationary, and a line sloping down is returning.
- For the whole trip, use totals. Average speed = total distance travelled ÷ total time taken.
Worked example
A student cycles from home. The graph has these turning points (time in hours, distance from home in km): (0, 0), (0.5, 12), (1, 12), (2, 30).
Segment 1, 0 to 0.5 h: distance rises from 0 to 12 km. Speed = 12 ÷ 0.5 = 24 km/h.
Segment 2, 0.5 h to 1 h: distance stays at 12 km. The student is stationary, so the speed is 0.
Segment 3, 1 h to 2 h: distance rises from 12 km to 30 km, a change of 18 km in 1 h. Speed = 18 ÷ 1 = 18 km/h.
Average speed for the whole 2 hours: total distance 30 km ÷ 2 h = 15 km/h.
Check: the average (15) is less than both moving speeds (24 and 18) because of the rest, which is sensible.
The mistake to watch for
A common slip is to divide the final distance by the final time for a segment that does not start at zero.
Mistaken answer for Segment 3: 30 ÷ 2 = 15 km/h
The student used the end point alone. That gives the average speed from the start of the trip, not the speed in that segment.
The correction is to use the change in both quantities for the segment: (30 − 12) ÷ (2 − 1) = 18 km/h. A segment’s speed always needs two points.
Check yourself
Try these, then open each answer.
1. Using the example graph, what is the speed in km/h during the stationary part?
Show answer
The distance does not change, so the change in distance is 0. Speed = 0 ÷ 0.5 = 0 km/h.
2. A straight line on a distance-time graph passes through (2, 10) and (6, 34), with distance in metres and time in seconds. Find the speed.
Show answer
Change in distance = 34 − 10 = 24 m. Change in time = 6 − 2 = 4 s. Speed = 24 ÷ 4 = 6 m/s.
3. A runner goes out 6 km in 30 minutes, rests for 10 minutes, then returns the 6 km in 40 minutes. Find the average speed for the whole trip in km/h.
Show answer
Total distance = 6 + 6 = 12 km. Total time = 30 + 10 + 40 = 80 min = 4/3 h. Average speed = 12 ÷ 4/3 = 12 × 3/4 = 9 km/h.
Where this leads next
Next, see how the area under a graph can carry meaning too in interpreting an area under a speed-time graph. You can explore graph shapes with the quadratic structure explorer and the graph-model explorer, then come back to the module page.
If you understand the graph in class but lose the method when a new one appears, our teachers can work through fresh graphs with you in online one-to-one Mathematics tuition.