Mathematics • Year 7 • Unit 4 • Lesson 6
Line Graphs
Build fluency with the five-step recipe: Scale → Plot → Join → Label → Title. Time always on the x-axis. Once a graph is built, describe its trend and use interpolation (safe) or extrapolation (risky) to estimate values.
1. I do — fully worked example
Read every line. Each step shows the question to ask and the reason for the answer.
Problem. A plant was 8 cm at Week 1 and 16 cm at Week 3. Use interpolation to find the height at Week 2.
Step 1 — Identify what we know and what we need.
Known: Week 1 = 8 cm, Week 3 = 16 cm. Need: Week 2 height.
Reason: Week 2 sits BETWEEN two known points, so interpolation is appropriate (and reliable).
Step 2 — Calculate the rate of change.
Change = 16 − 8 = 8 cm over 2 weeks → rate = 8 ÷ 2 = 4 cm per week.
Reason: we assume the plant grew at a steady rate between Week 1 and Week 3.
Step 3 — Apply the rate to Week 2.
Week 2 ≈ 8 + 4 = 12 cm.
Reason: one extra week at +4 cm/week from Week 1.
Answer: Week 2 ≈ 12 cm (interpolation — reliable, within data).
2. We do — fill in the missing steps
Plot the line graph for monthly rainfall (mm): Jan 45, Feb 38, Mar 62, Apr 55, May 30, Jun 18. Fill in each blank. 5 marks
Step 1 — Choose your scale. The largest value is _______ mm, so the y-axis should go up to at least _______ mm in steps of _______ mm.
Step 2 — Set up axes. The x-axis shows _______________ (Jan to Jun, equally spaced). The y-axis label must include units: "Rainfall (_____)".
Step 3 — Plot each point. Mark a dot at the correct height above each month: Jan→___, Feb→___, Mar→___, Apr→___, May→___, Jun→___.
Step 4 — Join the points. Connect with straight lines in the order ___________________________ (left to right).
Step 5 — Add a title. "_______________________________________________"
3. You do — independent practice
Eight graduated problems. Use the methods from sections 1 and 2.
Foundation — quick reads
3.1 A line graph shows daily temperatures (°C) for one week: Mon 18, Tue 22, Wed 28, Thu 25, Fri 20. Identify the peak temperature and the day it occurred. 1 mark
3.2 Using the same Mon–Fri data, identify the trough (lowest) temperature and its day. 1 mark
3.3 Why does TIME always go on the x-axis of a line graph? Answer in one sentence. 1 mark
3.4 Which axis label is correct: (a) "Rainfall" or (b) "Rainfall (mm)"? State which and give a one-line reason. 1 mark
Standard — describe and calculate
3.5 A city's average temperatures were: Jan 22 °C, Mar 26 °C, Jun 18 °C, Sep 14 °C, Dec 20 °C. Describe the overall trend in one or two sentences, naming the peak and trough months. 2 marks
3.6 A bike costs $500 in Year 1 and $300 in Year 3 (depreciation). Interpolate the value at Year 2. Show working. 2 marks
Extension — push your thinking
3.7 The plant in the worked example was 8 cm at Week 1 and 16 cm at Week 3. Extrapolate the height at Week 5, and explain in two sentences why this estimate is LESS reliable than the Week 2 interpolation. 3 marks
3.8 A line graph of a company's profit rises steeply Jan–Jun, then is flat Jul–Sep, then falls Oct–Dec. Describe each of the three sections in one short sentence (mention direction and approximate rate). 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Rainfall graph (We do)
Step 1: largest = 62 mm, y-axis to at least 70, steps of 10.
Step 2: x-axis shows Months; y-axis "Rainfall (mm)".
Step 3: Jan→45, Feb→38, Mar→62, Apr→55, May→30, Jun→18.
Step 4: connect Jan → Feb → Mar → Apr → May → Jun with straight lines.
Step 5: e.g. "Monthly Rainfall (mm) Jan–Jun".
3.1 — Peak temperature
28 °C on Wednesday (highest value in the week).
3.2 — Trough temperature
18 °C on Monday (lowest value).
3.3 — Why time on x-axis
Time is the independent variable — we choose when to measure, then plot what happens. By convention, the independent variable goes on the horizontal (x) axis.
3.4 — Axis label
(b) "Rainfall (mm)" is correct because every axis must include units. Just "Rainfall" doesn't tell the reader whether the values are mm, cm or inches.
3.5 — Trend description
"The temperature rose from 22 °C in January to a peak of 26 °C in March, then fell steadily to a trough of 14 °C in September, before rising again to 20 °C by December." Overall: a roughly cyclic pattern with the warmest month in early autumn (March) and the coldest in early spring (September) — consistent with the southern hemisphere.
3.6 — Bike depreciation (interpolation)
Change = 500 − 300 = $200 over 2 years → $100/year drop. Year 2 ≈ 500 − 100 = $400. (Equivalently: halfway between $500 and $300.)
3.7 — Plant at Week 5 (extrapolation)
Rate = 4 cm/week, so Week 5 ≈ 16 + (2 × 4) = 24 cm. This is LESS reliable than the Week 2 interpolation because Week 5 lies beyond the known data range. Plants don't grow at the same rate forever — growth often slows down as the plant matures, so the real Week 5 height could be much less than 24 cm.
3.8 — Profit in three sections
Jan–Jun: profit increases steeply (rapid growth).
Jul–Sep: profit is steady (flat line — no growth or fall).
Oct–Dec: profit decreases (the line falls from left to right).
Marking: 1 mark per section.