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Year 8 · Key Stage 3 · free KS3 maths worksheet

Linear and quadratic graphs

12 original questions, 39 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Four straight lines A, B, C and D are drawn on the grid.

Write down the equation of

  1. line A
  2. line B
  3. line C
  4. line D
−5−4−3−2−112345−5−4−3−2−112345OxyABCD
4 marks
Show answer
a) x = 3 b) y = -2 c) y = x d) y = -x
2

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)
3

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

−2−1123−8−7−6−5−4−3−2−11234Oxy
3 marks
Show answer
Straight line through (-2, -7), (0, -3) and (3, 3)
4

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

Work out the gradient of the line.

2 marks
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3
5

A straight line is drawn on the grid.

  1. Write down the y intercept of the line.
  2. Work out the gradient of the line.
  3. Write down the equation of the line in the form y = mx + c
−3−2−1123−6−5−4−3−2−112345678Oxy
3 marks
Show answer
a) 1 b) 3 c) y = 3x + 1
6

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
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a) c = -2 b) (0, -2)
7

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

Find the equation of the line.

3 marks
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y = -2x + 7
8

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
9

The graph shows the cost of hiring a bouncy castle for a party.

  1. Write down the y intercept of the graph. What does it tell you about the cost?
  2. Work out the gradient of the line. What does it tell you about the cost?
  3. Amara hires the bouncy castle for 4 hours. Work out the cost.
0123456020406080100120Time (hours)Cost (£)
4 marks
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a) 40: there is a fixed charge of £40 before any hours are added b) 10: the cost goes up by £10 for each extra hour c) £80
10
  1. Complete the table of values for y = x2 + 2x − 3
    x−4−3−2−1012
    y5−3−35
  2. On the grid, draw the graph of y = x2 + 2x − 3 for values of x from −4 to 2
−4−3−2−112−5−4−3−2−1123456Oxy
4 marks
Show answer
a) 0, -4, 0 b) smooth curve through (-4, 5), (-3, 0), (-2, -3), (-1, -4), (0, -3), (1, 0), (2, 5)
11

Kofi leaves home at 10:00 and cycles to the lake at a steady speed.

He arrives at the lake at 11:00. The lake is 12 km from his home.

He stays at the lake for 30 minutes.

He then cycles straight home at a steady speed and arrives home at 13:00.

  1. On the grid, draw a distance-time graph for Kofi's journey.
  2. Work out Kofi's speed on the way home, in kilometres per hour.
10:0010:3011:0011:3012:0012:3013:0002468101214TimeDistance from home (km)
4 marks
Show answer
a) line from (10:00, 0) to (11:00, 12), horizontal to (11:30, 12), line to (13:00, 0) b) 8 km/h
12

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

  1. Work out the gradient of the line.
  2. Find the equation of the line. Give your answer in the form y = mx + c
  3. Does the point (6, −7) lie on the line? You must show how you get your answer.
4 marks
Show answer
a) -2 b) y = -2x + 5 c) Yes, because -2 × 6 + 5 = -7

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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