Lesson 6 ~25 min Unit 4 · Data & Chance +85 XP

Line Graphs

Plot data over time, read trends, and estimate values using interpolation and extrapolation.

Today's hook: The stock market flashes a line graph every second — rising means profit, falling means loss. Scientists track global temperature with line graphs. Your fitness app shows steps-per-day as a line. Line graphs are the tool for data that changes over TIME.

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Think First

warm-up

Before you read on — quickly: Think of two real-life situations where you'd want to see how something changes over time. How would you show that data? Try to sketch the axes in your head, then check your reasoning as you go.

Record your answer in your workbook.

The Big Idea

+5 XP

A line graph shows how a variable changes over time. Data points are plotted on a grid and connected with straight lines. The slope of the line shows the rate of change — a steeper line means a faster change.

The horizontal axis (x-axis) always shows time. The vertical axis (y-axis) shows the measurement being tracked (temperature, height, price, etc.). Points are plotted then joined in order. A line rising from left to right shows an increase; a line falling shows a decrease.

Time on x-axis → Value on y-axis → Connect the dots

Time on the x-axis

Always put the time variable (days, months, years) on the horizontal axis.

Slope = rate of change

Steeper slope means faster change; flat line means no change.

Connect in order

Join points left to right — never skip over a point.

What You'll Master

objectives

Know

What a line graph is and when to use one
The names and roles of each axis
The meaning of trend, interpolation, extrapolation

Understand

Why slope indicates rate of change
Why time goes on the horizontal axis
Why extrapolation carries more risk than interpolation

Can Do

Plot a line graph from a table of values with correct labels
Describe increasing, decreasing and steady trends
Interpolate a value between two known points

Words You Need

vocabulary

Line graphA graph that uses points joined by lines to show change over time.

Time seriesData collected at regular time intervals (daily, monthly, yearly).

TrendThe overall direction a data set is moving (increasing, decreasing, or steady).

GradientHow steep a line is; represents the rate of change between two points.

InterpolationEstimating a value within the range of known data points.

ExtrapolationEstimating a value beyond the range of known data (less reliable).

Spot the Trap

heads-up

Wrong: Joining points on a bar chart with a line. Bar charts show separate categories — connecting the bars with a line is meaningless and misleading.

Right: Only use a line graph when the x-axis shows a continuous variable (usually time). For categories like "favourite colour", use a bar chart.

Wrong: Using a line graph to show the favourite sports of 30 students. Sports are categories — there's no continuous change between them.

Right: Before drawing, ask: "Does the x-axis show time or a continuous measurement?" If yes, a line graph is appropriate.

Plotting Points and Joining with Lines

+5 XP

To draw a line graph: (1) draw and label axes with units, (2) choose a suitable scale, (3) plot each point accurately, (4) join consecutive points with straight lines, (5) give the graph a title.

Example: Monthly rainfall (mm): Jan 45, Feb 38, Mar 62, Apr 55, May 30, Jun 18. Plot Jan–Jun on the x-axis with equal spacing. Rainfall (mm) on the y-axis from 0 to at least 70. Each month gets one dot at the correct height. Connect Jan→Feb→Mar→Apr→May→Jun with straight lines. Label both axes including units.

Scale → Plot → Join → Label → Title

Choose your scale first

Find the maximum value, round up, then decide how many grid lines you need.

Label with units

Every axis needs a label AND units (e.g. "Rainfall (mm)").

Plot then join

Mark all points first, then draw the connecting lines neatly.

Reading Trends

+5 XP

A trend is the overall direction of the data. Look at the graph from left to right: is it going up (increasing), going down (decreasing), staying flat (steady), or a mix? Also identify any peaks (highest points) and troughs (lowest points).

Describing a trend: Increasing — line rises from left to right (e.g. population over 20 years). Decreasing — line falls from left to right (e.g. petrol price falling). Steady — nearly flat line (e.g. a stable heart rate). A good trend description also mentions how quickly the change happened and any exceptions (a sudden spike or drop).

Direction + Rate + Peaks/Troughs = full description

Describe in context

Don't just say "it goes up" — say what went up and when.

Compare sections

Split the graph into sections and describe each separately.

Read the scale

Check the y-axis scale before reading off any value.

Interpolation vs Extrapolation

+5 XP

Interpolation estimates a value between two known data points on the graph. Extrapolation estimates a value beyond the data range by extending the trend line. Interpolation is reliable; extrapolation can be risky because the trend might change.

Example: A plant was 12 cm on Day 2 and 20 cm on Day 4. To interpolate Day 3: halfway between 12 and 20 = 16 cm (reliable, within known data). To extrapolate Day 6: extend the trend — estimate ~28 cm. But plants don't grow at a constant rate forever, so this is less reliable. Always add a caution when extrapolating.

Interpolation = within data (reliable) | Extrapolation = beyond data (risky)

Interpolation is safe

You're estimating where you already have data on either side.

Extrapolation is risky

Always flag it as an estimate — trends can change unexpectedly.

Use a dashed line

Convention: draw extrapolated sections as a dashed extension.

Watch Me Solve It · 3 examples

Watch Me Solve It · Plot a line graph

+15 XP per step

PROBLEM

Rainfall (mm) was recorded over 6 months: Jan 45, Feb 38, Mar 62, Apr 55, May 30, Jun 18. List the steps to draw this line graph correctly.

1

Set up the axes

x-axis: Months (Jan to Jun) equally spaced. y-axis: Rainfall (mm), scale 0 to 70 in steps of 10.

The maximum value is 62 mm, so the y-axis must go to at least 70 mm. Label both axes with titles and units.
2

Plot each data point

Jan→(Jan, 45), Feb→(Feb, 38), Mar→(Mar, 62), Apr→(Apr, 55), May→(May, 30), Jun→(Jun, 18)

Place a dot at the correct height for each month. Double-check your scale before marking each point.
3

Join points and add a title

Connect Jan→Feb→Mar→Apr→May→Jun with straight lines. Title: "Monthly Rainfall (mm) Jan–Jun"

Straight lines between consecutive points. Never skip a point or join non-consecutive months.

AnswerAxes with labels and units → 6 plotted points → connected with straight lines → descriptive title.

Watch Me Solve It · Describe a trend

+15 XP per step

PROBLEM

A line graph shows a city's average temperature: Jan 22°C, Mar 26°C, Jun 18°C, Sep 14°C, Dec 20°C. Describe the overall trend and identify the peak and trough.

1

Identify the overall direction

Jan→Mar: increases (22 to 26). Mar→Sep: decreases (26 to 14). Sep→Dec: increases (14 to 20).

The graph goes up then down then up — it's not a simple trend. Describe each section separately.
2

Identify peak and trough

Peak = 26°C in March. Trough = 14°C in September.
3

Write a full description in context

"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 recovering to 20°C by December."

A good description includes direction, actual values, and months. Always write in the context of the data.

AnswerPeak: 26°C (March). Trough: 14°C (September). Overall: rises then falls then rises again.

Watch Me Solve It · Interpolate and extrapolate

+15 XP per step

PROBLEM

A plant was 8 cm at Week 1 and 16 cm at Week 3. Interpolate its height at Week 2, and extrapolate its likely height at Week 5. State which is more reliable.

1

Interpolate Week 2

Change from Week 1 to 3 = 16 − 8 = 8 cm over 2 weeks = 4 cm/week. Week 2 ≈ 8 + 4 = 12 cm

Week 2 is between the two known points, so we divide the change evenly. This estimate is reliable.
2

Extrapolate Week 5

Assuming 4 cm/week continues: Week 5 ≈ 16 + (2 × 4) = 24 cm (with caution)
3

Compare reliability

Interpolation (Week 2) is more reliable. Extrapolation (Week 5) assumes the trend continues, but plants may slow their growth.

We have no data beyond Week 3, so the Week 5 estimate could easily be wrong.

AnswerWeek 2 ≈ 12 cm (interpolation, reliable). Week 5 ≈ 24 cm (extrapolation, less reliable).

Common Pitfalls

heads-up

Not labelling axes with units

A graph without units is nearly useless. Writing "Temperature" on the y-axis is incomplete — is it Celsius or Fahrenheit? Writing "Rainfall (mm)" is correct. Examiners deduct marks for missing units.

Fix: Before drawing, write axis labels including units in brackets (e.g. "Rainfall (mm)"). Then add your title.

Connecting non-consecutive points

Students sometimes draw lines between non-adjacent points, creating X-shaped crossings. Lines should only connect adjacent time periods in order.

Fix: Work left to right, connecting each dot only to the next dot in time. Never skip a time period.

Extrapolating too far beyond the data

Extending a trend far beyond the last data point assumes the pattern never changes. In reality, stock prices crash, temperature patterns shift, and plants stop growing.

Fix: Only extrapolate a short distance, and always add the qualifier "assuming the trend continues" in your answer.

Copy Into Your Books

Line Graph Basics

Time on the x-axis; measurement on the y-axis
Plot each point, then join with straight lines (left to right)
Label axes with titles AND units
Add a descriptive title to the whole graph

Reading Trends

Increasing: line rises left to right
Decreasing: line falls left to right
Steady: line is nearly flat
Peak = highest point; Trough = lowest point

Interpolation

Estimating within the known data range
Use the gradient between two known points
More reliable than extrapolation

Extrapolation

Estimating beyond the known data range
Extend the trend line (draw as dashed)
Less reliable — always add a caution
"Assuming the trend continues..."

How are you completing this lesson?

Brain Trainer · 4 problems

Brain Trainer · Line Graphs

4 problems

Four drill problems to sharpen your line graph skills. Work each, then reveal the answer.

1 Temperature was 18°C, 22°C, 28°C, 25°C, 20°C over 5 consecutive days (Mon–Fri). What was the peak temperature and on which day?

The peak is the highest value. Reading the data: 18, 22, 28, 25, 20. Peak = 28°C on Wednesday
2 Looking at Mon (18°C) to Fri (20°C): what happened to the temperature overall across the week?

Overall the temperature was slightly higher on Friday (20°C) than Monday (18°C). However the trend was not steadily increasing — it rose mid-week then fell. Overall slight increase (+2°C), but with a peak on Wednesday
3 Why is extrapolation risky? Give one specific reason.

Extrapolation assumes the current trend will continue unchanged, but real-world data rarely follows a perfectly consistent pattern. For example, a company's profits might grow for 5 years then suddenly fall due to a competitor. The future trend may change, making predictions unreliable
4 Name 2 situations where a line graph is the most appropriate display.

Any two of: daily temperature over a month, stock prices over a year, a student's test scores across a term, population of a city over decades, rainfall totals month by month. Key: must involve a measurement that changes over time. Any two time-series examples

Complete in your workbook.

Quick Check · 5 questions

Which statement best describes a line graph?

+10 XP

On a line graph, where does time go?

+10 XP

Which of these should NOT be shown as a line graph?

+10 XP

Why is interpolation more reliable than extrapolation?

+10 XP

What does a steep upward slope on a line graph indicate?

+10 XP

Show Your Working · 3 questions

Show Your Working

9 marks total

Apply Medium 3 MARKS

Q6. A student recorded the number of pages read each day: Mon 12, Tue 18, Wed 9, Thu 22, Fri 15. Describe the trend shown if these were plotted on a line graph, including the peak and trough day.

Answer in your workbook.

Understand Easy 2 MARKS

Q7. A graph shows a car's speed: at 2 minutes the speed was 40 km/h and at 4 minutes the speed was 60 km/h. Interpolate the speed at 3 minutes. Show your working.

Answer in your workbook.

Evaluate Hard 4 MARKS

Q8. A friend says: "I'll use extrapolation to predict this city's population in 100 years based on 5 years of data." Give two reasons why this prediction is unreliable, and suggest what they should do instead.

Answer in your workbook.

Comprehensive Answers

Quick Check

1. B — A line graph plots data over time and joins points with lines.

2. A — Time goes on the horizontal (x) axis.

3. C — Favourite sports are categories — use a bar chart.

4. D — Interpolation estimates within the known range, so neighbouring data exists on both sides.

5. A — Steep upward slope = rapid increase in the value.

Show Your Working Model Answers

Q6 (3 marks): The trend was variable (not steadily increasing or decreasing) [1]. Peak: Thursday with 22 pages [1]. Trough: Wednesday with 9 pages [1].

Q7 (2 marks): Change in speed = 60 − 40 = 20 km/h over 2 minutes = 10 km/h per minute [1]. Speed at 3 min = 40 + 10 = 50 km/h [1].

Q8 (4 marks): Reason 1: 5 years of data is a very short sample — long-term trends may be completely different from short-term trends [1]. Reason 2: Many unpredictable events (pandemics, economic changes, wars, natural disasters) can alter population growth over 100 years [1]. Better approach: Gather more historical data (50+ years) [1] and use multiple statistical models, not just a simple linear extrapolation [1].

Stretch Challenge · +25 XP, +10 coins

The Temperature Puzzle

A city recorded midday temperatures (in °C) over 8 days: 24, 26, 29, 27, 23, 20, 18, 22. (a) Identify the overall trend across the 8 days. (b) Between which two consecutive days was the temperature drop the greatest? Calculate the exact drop. (c) Interpolate the temperature between Days 7 and 8 if there had been a Day 7.5. (d) If the trend from Days 5–7 continued, extrapolate the temperature for Day 9 and explain why this is uncertain.

Reveal solution

(a) Overall: rises from Day 1 to 3 (peak 29), then decreases to Day 7 (18), with a slight recovery on Day 8. Generally decreasing trend after Day 3. (b) Days 4 to 5: 27→23 = drop of 4°C. Wait — also check Days 5→6: 23→20 = 3°C, Days 6→7: 20→18 = 2°C. Largest single-day drop: Days 4→5 = 4°C. (c) Day 7.5 = midpoint of Days 7 and 8 = (18+22)/2 = 20°C. (d) Days 5→7: decreasing by ~2.5°C/day, so Day 9 ≈ 18 − 5 = 13°C. Uncertain because the recovery on Day 8 already breaks this trend.

Quick Review

Line graphs show change over time

Time on x-axis; measurement on y-axis. Points joined with lines in order.

Axes need labels AND units

"Rainfall (mm)" not just "Rainfall". Missing units = lost marks.

Trend = overall direction

Increasing, decreasing, steady — or describe each section if it changes.

Peak and trough

Peak = highest point; trough = lowest point. State the exact value and time.

Interpolation is reliable

Estimating within the data range. Both sides are known.

Extrapolation is risky

Estimating beyond the data. Always say "assuming the trend continues".

Interactive: Line Graph Builder

Plot your own data on this interactive grid and see how trends form in real time.

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