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GCSE Maths revision · Algebra

Straight-line graphs

Foundation and Higher

The idea

A straight line y=mx+cy = mx + c has gradient mm and crosses the yy-axis at cc. Gradient =change in ychange in x= \frac{\text{change in } y}{\text{change in } x}.

  1. For a table of values, substitute three xx-values and plot the points.
  2. For the gradient, take two points and divide the rise by the run.
  3. A line going down from left to right has a negative gradient.

Watch out Gradient is the change in yy over the change in xx, not the other way up.

See it worked

Worked exampleNon-calculator2 marks

A straight line passes through (1, 3) and (5, 11). Work out its gradient.

  1.  11−35−1\frac{11-3}{5-1}
  2. Gradient = change in y ÷\div change in x.
  3. The gradient is (11 −- 3)/(5 −- 1) = 8/4 = 2.

Answer 22

Your turn

Question 1Non-calculator3 marks

A straight line has equation y=2x−1y = 2x - 1.

(a) Work out the value of yy when x=−1x = -1.

(b) Write down the gradient of the line.

(c) Write down the yy-coordinate of the point where the line crosses the yy-axis.

Question 2Non-calculator4 marks

A table of values for a straight line gives y = 7, 4, 1 and −2 when x = −1, 0, 1 and 2.

(a) Write down the y-intercept of the line.

(b) Find the gradient of the line.

(c) Write down the equation of the line.

Question 3Calculator allowed2 marks

Find the coordinates of the point where the line 4x + 3y = 18 crosses the x-axis.

In past papers

111 official questions in 100 papers since 2017. The latest:

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