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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Gradient and y-intercept of a straight line

Reading m and c from y = mx + c.

18 original questions, 42 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 has equation y = 3x − 2

  1. Write down the gradient of the line.
  2. Write down the coordinates of the point where the line crosses the y-axis.
2 marks
Show answer
a) 3 b) (0, -2)
2

A straight line has equation y = 5x + 2

Write down the gradient of the line.

1 mark
Show answer
5
3

A straight line has gradient 4 and passes through the point (0, 5).

Find the equation of the line.

2 marks
Show answer
y = 4x + 5
4

Here are the equations of three straight lines.

Line A: y = 2x + 1

Line B: y = 3x − 2

Line C: y = 2x − 5

  1. Which two lines are parallel?
  2. Which line passes through the point (0, −2)?
2 marks
Show answer
a) A and C b) B
5

A straight line has equation y = 7 - 2x

Write down the gradient of the line.

1 mark
Show answer
-2
6

Here is a table of values for y = 2x − 3.

x−10123
y
  1. Complete the table of values.
  2. Write down the gradient of the line.
3 marks
Show answer
a) -5, -3, -1, 1, 3 b) 2
7

The equation of a straight line is y = 4x − 1.

For each point, say whether it lies on the line. Show your working.

  1. (3, 11)
  2. (2, 8)
2 marks
Show answer
a) yes b) no
8

Here are the equations of four straight lines.

A: y = 4x + 3    B: y = 3x − 7    C: y = −3x + 4    D: 3y = x + 4

Which line is parallel to y = 3x + 4?

1 mark
Show answer
B
9

A straight line has equation 2y = 6x + 10

  1. Write down the gradient of the line.
  2. Write down the coordinates of the point where the line crosses the y-axis.
2 marks
Show answer
a) 3 b) (0, 5)
10

On the grid, draw the graph of y = 3x − 2 for values of x from −1 to 3.

−2−11234−8−7−6−5−4−3−2−112345678Oxy
3 marks
Show answer
Straight line through (-1,-5), (0,-2), (1,1), (2,4), (3,7)
11

A taxi company charges a fixed fee plus a cost for each kilometre travelled. The table shows the cost, in pounds, for some journeys. The points lie on a straight line graph.

Distance (km)0246
Cost (£)371115
  1. Work out the gradient of the line.
  2. What does the gradient represent?
  3. What does the y-intercept represent?
3 marks
Show answer
a) 2 b) The cost per kilometre, £2 per km c) The fixed fee of £3 (cost when distance is 0)
12

The points A (2, 3) and B (6, k) lie on a straight line with gradient 2.

Work out the value of k.

3 marks
Show answer
11
13

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
14

A straight line has gradient 4 and passes through the point (1, 7).

Find the equation of the line.

3 marks
Show answer
y = 4x + 3
15

A straight line has gradient −2 and crosses the y-axis at (0, 5).

Work out the x-coordinate of the point where the line crosses the x-axis.

3 marks
Show answer
2.5
16

Here is a table of values for y = 12x + 2

x: −4, −2, 0, 2, 4

y: 0, ?, 2, ?, 4

  1. Work out the two missing values of y.
  2. Write down the gradient of the line.
3 marks
Show answer
a) 1 and 3 b) 1/2
17

A straight line passes through the points (0, −1) and (4, 7).

  1. Work out the gradient of the line.
  2. Write down the equation of the line in the form y = mx + c
3 marks
Show answer
a) 2 b) y = 2x - 1
18

The straight line y = 4x + c passes through the point (3, 10).

  1. Find the value of c.
  2. Write down the coordinates of the point where the line crosses the y-axis.
3 marks
Show answer
a) c = -2 b) (0, -2)

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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