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.