Relationships in Authentic Graphs

Part A — 5 × 2-mark questions

1. An electricity-use graph rises steeply between 6 pm and 9 pm. Describe the relationship between time and electricity usage during this period.
2. A distance-from-home graph is horizontal from 8:10 am to 8:20 am. What does this indicate about the traveller?
3. A temperature graph has a steep negative slope from 3 am to 5 am. Describe the change.
4. A fitted line is y = 3x + 12. Explain what the slope 3 means.
5. A distance-time graph is steep from 0–5 min and shallow from 5–10 min. Compare the traveller's speeds.

Part B — 5 × 5-mark questions

6. A building's electricity use is low overnight, rises sharply at 7 am, is nearly constant from 9 am–5 pm, peaks at 6 pm, then declines. Describe the relationship, identify constant and rapid-change periods, suggest plausible causes using cautious language, and tell the day's story.
7. A travel graph shows a steep rise away from home, a 10-minute horizontal segment, then a shallow fall back to zero. Describe each segment, compare speeds, explain the stop and interpret the whole journey.
8. A liquid-volume graph rises slowly, then rapidly, then flattens. Describe how the rate changes, explain what each slope means, and give one plausible real-world filling or pouring story.
9. A straight-line model predicts house price from floor area. Explain what slope and intercept mean, what points close to the line suggest, what an outlier is, and why a steeper slope does not automatically mean a stronger relationship.
10. An evaporation-rate graph is slow in the morning, rises rapidly around midday and falls late afternoon. Describe the relationship, identify fastest change, suggest environmental factors and explain how the graph could inform water-management decisions.

Part C — Enrichment

A community monitors evaporation from a water source. The graph shows a steep rise during a hot period, a sudden drop after cloud cover, and a near-constant rate during evening cooling. Explain the graph, distinguish observations from possible causes, identify each change in slope, and propose what extra measurements would help test the explanation. Then explain how graph interpretation can support sustainable local water-resource decisions.