Mathematics • Year 8 • Unit 4 • Lesson 6
Line Graphs in the Real World
Apply line graphs to real situations: weather records, sales forecasts, sports performance, population trends, and stock prices — describe trends, estimate values, and judge reliability.
1. Word problems
Each problem uses ideas from Lesson 6. Show your working — a single answer with no working only earns half marks.
1.1 — Weekly weather. Daily maximum temperature (°C) Mon–Sun: 22, 24, 26, 28, 30, 27, 25.
(a) Describe the trend in one sentence.
(b) On which day was the maximum temperature highest, and what was it?
(c) Estimate the temperature halfway between Thursday and Friday (i.e. Thursday evening) using interpolation. 3 marks
1.2 — Streaming subscribers. A streaming service records millions of subscribers each quarter for 6 quarters: Q1: 50, Q2: 55, Q3: 61, Q4: 68, Q5: 76, Q6: 85.
(a) Describe the trend.
(b) Estimate the number of subscribers at Q7 using extrapolation. Assume the increase continues at the average rate.
(c) State one reason why this extrapolation might be unreliable. 3 marks
1.3 — Plant growth. A student measures a plant's height (cm) weekly: Week 1 = 4, Week 2 = 7, Week 3 = 11, Week 4 = 16, Week 5 = 22.
(a) Plot the data mentally — describe the trend.
(b) Estimate the height at the end of Week 3.5 by interpolation.
(c) Predict the height at Week 8 by extrapolation. Comment on whether this prediction is sensible. 3 marks
1.4 — Reading from a graph. A line graph of pet shop weekly revenue shows: Mon $400, Tue $520, Wed $480, Thu $610, Fri $720, Sat $880, Sun $750.
(a) Describe the overall trend in one or two sentences (mention any dips).
(b) On which day was revenue highest?
(c) Identify one day where revenue dropped from the previous day. 3 marks
1.5 — Chart-type choice. A school principal wants to track total student enrolment each year for the past 10 years, and a parent wants to see what percentage of students are in each year level for THIS year.
(a) Which display suits the principal's question: line graph, bar chart, or pie chart? Justify.
(b) Which display suits the parent's question? Justify. 3 marks
2. Explain your thinking
This question is about communication, not just answers. Use full sentences. 4 marks
2.1 A weather website extrapolates from 7 days of data to forecast the temperature 30 days from now and states "We are 95% sure of this number." In your own words, explain (i) why this kind of long-range extrapolation is risky, (ii) what types of unexpected events could break the trend, and (iii) what shorter prediction would be more trustworthy. Use the term extrapolation somewhere in your answer.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Weekly weather
(a) Temperature increased from Monday to Friday, peaked at 30°C on Friday, then decreased back to 25°C by Sunday.
(b) Friday, 30°C.
(c) (28 + 30) ÷ 2 = 29°C.
1.2 — Streaming subscribers
(a) Increasing trend — the growth rate is also accelerating: differences are 5, 6, 7, 8, 9 (millions) per quarter.
(b) Q7 ≈ 85 + 10 = 95 million (assuming the increase grows by 1 each quarter).
(c) Unreliable because the growth could level off due to market saturation, new competition, or a price change.
1.3 — Plant growth
(a) Increasing — growth is accelerating each week (+3, +4, +5, +6).
(b) Week 3.5 ≈ (11 + 16) ÷ 2 = 13.5 cm.
(c) Week 8 ≈ 46 cm (extending the +3, +4, +5, +6, +7, +8, +9 pattern). This is extrapolation and may be unreliable — most plants slow their growth as they mature, and water/light limits will eventually cap height.
1.4 — Pet shop revenue
(a) Revenue increased overall through the week, with a dip on Wednesday and another drop on Sunday after the Saturday peak.
(b) Highest day = Saturday ($880).
(c) Wednesday (520 → 480 = drop of $40) or Sunday (880 → 750 = drop of $130).
1.5 — Chart-type choice
(a) Line graph — total enrolment over 10 years is continuous time-series data; a line graph shows the trend clearly.
(b) Pie chart — parts of a whole (each year level is a percentage of all students this year), with around 6 year levels at most.
2.1 — Explain your thinking (sample response)
Long-range extrapolation based on only 7 days of data is risky because the underlying trend can easily change beyond the data range — 30 days is more than four times the length of the observed period. Unexpected events like a cold front, a storm system, an early seasonal change, or a heatwave can completely break the trend in a single day. A shorter forecast — say, 2 to 5 days ahead — would be much more trustworthy because the recent trend is more likely to continue over a short interval, and weather models are calibrated for near-term predictions. Claiming "95% certainty" for a 30-day extrapolation overstates the reliability of any forecast based on 7 points of data.
Marking: 1 mark for explaining why long-range extrapolation is risky; 1 mark for naming concrete trend-breakers; 1 mark for proposing a shorter, more reliable horizon; 1 mark for clear, full-sentence answer using "extrapolation".