Straight-Line Graphs — Grade 9 & 10 Maths (CAPS)

Every non-vertical straight line is described by y = mx + c. Once you know what m and c do, you can sketch any line and read any graph.

Also known as: slope · gradient and y-intercept · linear graphs · y = mx + c · slope-intercept form

A straight-line graph shows a relationship that changes at a constant rate. Every straight line that is not vertical has an equation of the form y = mx + c (a vertical line is x = k), and the whole topic comes down to understanding what the two letters m and c mean.

1c is where the line starts

c is the y-intercept — the point where the line crosses the vertical axis (where x = 0). If the equation is y = 2x + 3, the line crosses the y-axis at 3.

2m is how steep it is

m is the gradient — how much y changes for every 1 unit across. Gradient = (change in y)/(change in x). A positive m slopes up to the right; a negative m slopes down.

The line y = mx + c: c is where it cuts the y-axis; the gradient m is rise ÷ run.

Worked ExampleWorked example: sketch y = 2x − 1

1
Start at the y-intercept: c = −1, so plot (0 ; −1).
This is the guaranteed starting point.
2
Use the gradient m = 2 = 2/1: go 1 right and 2 up to (1 ; 1).
Gradient tells you the next point from the intercept.
3
Join the two points with a straight line and extend it.
Two points fully fix a straight line.

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To find the x-intercept (where the line crosses the horizontal axis), set y = 0 and solve for x. For y = 2x − 1 that gives x = 1/2.

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Don't confuse the intercepts. The y-intercept comes from x = 0; the x-intercept comes from y = 0. Mixing them up is a classic slip.

Straight-line graphs are the gateway to all of functions in Grades 10–12, and analytical geometry is built directly on gradient and intercepts — so a solid grip here pays off for years.

Practice exercises

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

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
For y = 3x + 2, give the gradient and y-intercept.
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Gradient 3, y-intercept 2
2
For y = −x + 5, where does it cross the y-axis?
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At (0 ; 5)
3
Find the y-intercept of y = 4x − 7.
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−7, i.e. the point (0 ; −7)
4
Find the x-intercept of y = 2x − 6.
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Set y = 0: 2x − 6 = 0 → x = 3