Robinson Tuition
Grade 6 · Higher · free GCSE maths worksheet

Equation of a line through two points

Finding m then c.

14 original questions, 46 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

A straight line passes through the points (0, -3) and (2, 5).

Find the equation of the line.

Give your answer in the form y = mx + c

3 marks
Show answer
y = 4x - 3
2

A straight line passes through the points (1, 7) and (3, 13).

Find the equation of the line.

Give your answer in the form y = mx + c

3 marks
Show answer
y = 3x + 4
3

A straight line has gradient -2 and passes through the point (3, 1).

Find the equation of the line.

3 marks
Show answer
y = -2x + 7
4

A straight line passes through the points A (2, 5) and B (6, 17).

Work out the gradient of the line.

2 marks
Show answer
3
5

A straight line passes through the points (-2, 1) and (2, 9).

Find the equation of the line.

Give your answer in the form y = mx + c

3 marks
Show answer
y = 2x + 5
6

A straight line passes through the points P (-3, 4) and Q (5, -8).

Work out the gradient of the line.

2 marks
Show answer
-32
7

A straight line passes through the points (4, -1) and (6, -7).

Find the equation of the line.

3 marks
Show answer
y = -3x + 11
8

A straight line passes through the points (2, 1) and (6, 4).

Find the equation of the line.

Give your answer in the form y = mx + c.

3 marks
Show answer
y = 3x/4 - 1/2
9

A straight line passes through the points (-3, 5) and (3, 1).

Find the equation of the line.

3 marks
Show answer
y = -2x/3 + 3
10

A straight line passes through the points (-2, -1) and (4, 8).

  1. Find the equation of the line.
  2. Show that the point (8, 14) lies on the line.
4 marks
Show answer
a) y = 3x/2 + 2 b) When x = 8, y = 14, so the point lies on the line
11

A straight line passes through A(-4, 3) and B(6, -2).

  1. Find the equation of the line.
  2. Find the coordinates of the point where the line crosses the x-axis.
4 marks
Show answer
a) y = -x/2 + 1 b) (2, 0)
12

A mobile phone company charges £C for d GB of data a month. The cost is a straight line graph. The cost for 5 GB is £14 and the cost for 20 GB is £35.

  1. Find a formula for C in terms of d.
  2. What does the gradient of the line represent?
4 marks
Show answer
a) C = 1.4d + 7 b) The cost of each extra GB of data, £1.40
13

A is the point (2, 3) and B is the point (6, 11).

M is the midpoint of AB.

Find the equation of the straight line with gradient 12 that passes through M.

4 marks
Show answer
y = x2 + 5
14

A is the point (1, 2) and B is the point (9, 18).

The point P lies on AB so that AP : PB = 3 : 1

Show that P lies on the straight line with equation y = 2x

5 marks
Show answer
P = (7, 14) and 2 x 7 = 14, so P lies on y = 2x

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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