The idea, step by step
Read what the axes measure
First identify the quantities, units and scale. Then describe graph changes in the situation. A rising distance-from-home graph means the traveller is farther from home. A flat section means that measured distance stays unchanged.
The supplied journey log is example data. From minute 2 to minute 5 it remains at 6 km. In a simple outward-journey model this may represent a stop; the graph alone does not describe every action of the traveller.
| Time (min) | Distance from home (km) |
|---|---|
| 0 | 0 |
| 2 | 6 |
| 5 | 6 |
| 7 | 10 |
Compare intervals and avoid overclaims
A greater vertical change over a much longer time does not automatically mean a faster change. Compare equal time intervals where possible, and state the interval you used.
A graph ending at minute 7 does not establish what happened at minute 20. Long-range predictions depend on assumptions. A straight line between readings is a model, not proof of every intermediate value.
A common trap
Assuming a flat distance-from-home graph means the traveller is at home.
Instead: Read the vertical value: a flat section means an unchanged distance, not necessarily zero.
See the thinking
A flat interval
What happens from minute 2 to minute 5 in the journey log?
| Time (min) | Distance from home (km) |
|---|---|
| 0 | 0 |
| 2 | 6 |
| 5 | 6 |
| 7 | 10 |
- Both readings are 6 km.
- The change in distance from home is 0 km.
- The time interval is 5−2=3 minutes.
Compare cooling
Temperatures are 80,65,55,50°C at times 0,2,4,6 min. When is the greatest two-minute fall?
| Time (min) | Temperature (°C) |
|---|---|
| 0 | 80 |
| 2 | 65 |
| 4 | 55 |
| 6 | 50 |
- The falls are 15°C, 10°C and 5°C.
- Each interval lasts 2 minutes.
- The largest fall is 15°C.
Check your understanding
A distance-from-home graph is flat at 5 km. Is the person at home?
Show answer
No. The distance from home remains 5 km.
At home the graph's distance value would be 0 km.
Your turn
6 questions · 13 marks · Work at your own pace.
Read the questions online
- Using the journey log, give the distance from home at minute 7.2 marks
Journey log supplied for this example Time (min) Distance from home (km) 0 0 2 6 5 6 7 10 - How much farther from home is the traveller at minute 7 than at minute 5?2 marks
Journey log supplied for this example Time (min) Distance from home (km) 0 0 2 6 5 6 7 10 - For how long is the supplied journey graph flat?2 marks
- A graph has time in hours horizontally and distance in kilometres vertically. Explain (2,90).2 marks
- Use the cooling readings to find the total temperature fall in six minutes.2 marks
Supplied cooling readings Time (min) Temperature (°C) 0 80 2 65 4 55 6 50 - Plant height was recorded for four weeks. Why may continuing the same line to week 30 be unreliable?3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Using the journey log, give the distance from home at minute 7.2 marks
Journey log supplied for this example Time (min) Distance from home (km) 0 0 2 6 5 6 7 10 Read (7,10).
10 km. - How much farther from home is the traveller at minute 7 than at minute 5?2 marks
Journey log supplied for this example Time (min) Distance from home (km) 0 0 2 6 5 6 7 10 10−6=4.
4 km. - For how long is the supplied journey graph flat?2 marks
It is flat from minute 2 to minute 5.
5−2=3.
3 minutes. - A graph has time in hours horizontally and distance in kilometres vertically. Explain (2,90).2 marks
Use the horizontal label for the first coordinate.
After 2 hours the recorded/modelled distance is 90 km. - Use the cooling readings to find the total temperature fall in six minutes.2 marks
Supplied cooling readings Time (min) Temperature (°C) 0 80 2 65 4 55 6 50 80−50=30.
30°C. - Plant height was recorded for four weeks. Why may continuing the same line to week 30 be unreliable?3 marks
The prediction assumes the same growth continues far beyond the observations.
Later growth may have a different rate, and the four-week data do not establish long-term behaviour.
Curriculum reference & lesson scope
Australian Curriculum v9.0 / South Australian Curriculum
Year 7 coordinate, pattern and authentic-graph interpretation scope. Includes prerequisite four-quadrant plotting; formal gradient/intercept techniques are not required here.
Official curriculum source ↗