Interpreting & Drawing Graphs

Reading global graphs — increasing, decreasing and constant sections, linear versus non-linear, maximum and minimum points, and discrete versus continuous data — plus plotting points on the Cartesian plane, with diagrams and a quiz.

A graph tells a story with a picture. In Grade 8 you must be able to read that story — describing what is happening — and to draw a graph from a description.

1Increasing, decreasing and constant

The three basic behaviours: a graph can go up (increasing), go down (decreasing) or stay level (constant).

Increasing — as you move right, the graph rises (the quantity is growing).
Decreasing — as you move right, the graph falls.
Constant — the graph is a flat horizontal line; nothing is changing.

2Linear or non-linear

A linear graph is a perfectly straight line — the quantity changes by the same amount each time. A non-linear graph curves, meaning the rate of change itself is changing.

3Maximum and minimum points

A maximum is the highest point the graph reaches (where it stops rising and starts falling); a minimum is the lowest point. In a story graph these are the turning points — the hottest moment of the day, the furthest point of a journey.

4Discrete or continuous

Discrete data can only take separate, countable values — the number of learners in a class. It is plotted as separate dots, not joined.
Continuous data can take any value in a range — temperature or height. It is drawn as an unbroken line.

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Ask yourself: "can this quantity be half of one?" You cannot have half a learner (discrete), but you can have half a degree (continuous).

5Reading a story from a graph

Worked ExampleDescribe a journey: the graph rises steadily, flattens, then falls steeply

1
Rising steadily — the cyclist is riding away from home at a steady speed.
Increasing distance over time.
2
Flat section — the distance is not changing, so the cyclist has stopped to rest.
Constant means no change.
3
Falling steeply — the cyclist returns home, and quickly.
Decreasing distance; a steeper line means a faster speed.

6Plotting points on the Cartesian plane

Points are written as ordered pairs (x ; y). The first number is the horizontal position, the second the vertical one. Always go across first, then up.

Worked ExamplePlot the point (3 ; 2)

1
Start at the origin (0 ; 0).
Where the two axes cross.
2
Move 3 units right along the x-axis.
The x-value comes first.
3
Then move 2 units up, and mark the point.
The y-value is vertical.

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Never swap the order: (3 ; 2) and (2 ; 3) are two different points. Across before up, every time.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
A graph goes up steadily from left to right. Describe it in one word.
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Increasing
2
What does a flat horizontal section of a graph tell you?
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The quantity is constant — it is not changing.
3
Is a perfectly straight-line graph linear or non-linear?
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Linear
4
Is 'the number of cars in a parking lot' discrete or continuous?
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Discrete — you can only count whole cars.
5
Is 'the temperature during the day' discrete or continuous?
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Continuous — it can take any value.
6
What is the name of the highest point on a graph?
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The maximum
7
How do you plot (5 ; 1)?
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From the origin go 5 right, then 1 up.
8
A distance-time graph is flat for 10 minutes. What is happening?
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The person is stationary (not moving) for those 10 minutes.