Grade 9 Linear Graphs

Grade 9 graphs: plotting straight lines, gradient, x- and y-intercepts, y = mx + c, and interpreting graphs of real situations, with worked examples.

A linear graph is a straight line, and its equation can be written as y = mx + c. In Grade 9 you plot straight lines from a table of values, find where they cut the axes, and work out the gradient, which tells you how steep the line is.

You also read and draw graphs of real situations, such as the cost of a taxi trip or the distance travelled over time, and describe what the shape of the graph tells you. Grade 10 builds on this with parabolas, hyperbolas and exponential graphs.

Key concepts

  • Plotting points and drawing a straight line from a table
  • Gradient m = change in y ÷ change in x
  • y-intercept (where x = 0) and x-intercept (where y = 0)
  • y = mx + c: m is the gradient and c is the y-intercept
  • Parallel lines have the same gradient
  • Interpreting graphs: increasing, decreasing and constant

Worked examples

What is the gradient of the line y = −3x + 5?

In y = mx + c the gradient is m, so the gradient is −3. The line slopes downwards from left to right.

Where does y = 2x − 6 cut the x-axis?

On the x-axis y = 0: 2x − 6 = 0, so x = 3. The x-intercept is (3; 0). The y-intercept is (0; −6).

Find the gradient of the line through (1; 2) and (3; 8).

m = (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.

A taxi charges R20 plus R8 per kilometre. Write an equation and find the cost of a 12 km trip.

Cost y = 8x + 20, where x is the distance in km. For 12 km: y = 8(12) + 20 = R116. The gradient (8) is the cost per km.

Common mistakes

  • Dividing the change in x by the change in y when finding the gradient.
  • Mixing up the x-intercept and the y-intercept.
  • Plotting points with x and y swapped.
  • Joining plotted points with a wobbly freehand line instead of a ruler.

Exam tips

  • Use at least three points; if they don't line up, check your table.
  • Label both axes and write the equation next to the line.
  • Find intercepts by setting x = 0 or y = 0.

Frequently asked questions

What does a negative gradient mean?

The line goes down from left to right: as x increases, y decreases.

How do I draw a line quickly from y = mx + c?

Plot the y-intercept (0; c), then use the gradient: for m = 2, go 1 unit right and 2 units up to get a second point.

What does a horizontal line on a distance–time graph mean?

The distance isn't changing, so the object is standing still.

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