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Gradient of a line practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of gradient of a line questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

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Question 1 Easy

Work out the gradient of the line through (0, 4) and (2, 0).

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Answer: -2

  1. Change in y = 0 - 4 = -4, change in x = 2 - 0 = 2.
  2. Gradient = -4 / 2 = -2.
  • Method (1): Change in y = 0 - 4 = -4, change in x = 2 - 0 = 2.
  • Accuracy (1): Gradient = -4 / 2 = -2.

Question 2 Easy

Work out the gradient of the line through (1, 1) and (4, 10).

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Answer: 3

  1. Change in y = 10 - 1 = 9, change in x = 4 - 1 = 3.
  2. Gradient = 9 / 3 = 3.
  • Method (1): Change in y = 10 - 1 = 9, change in x = 4 - 1 = 3.
  • Accuracy (1): Gradient = 9 / 3 = 3.

Question 3 Medium

Work out the change in y from (1, 2) to (5, 10).

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Answer: 8

  1. Difference in y-coordinates: 10 - 2.
  2. Result is 8.
  • Method (1): Difference in y-coordinates: 10 - 2.
  • Accuracy (1): Result is 8.

Question 4 Medium

Work out the change in y from (2, 6) to (5, 0).

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Answer: -6

  1. Difference in y-coordinates: 0 - 6.
  2. Result is -6.
  • Method (1): Difference in y-coordinates: 0 - 6.
  • Accuracy (1): Result is -6.

Question 5 Hard

Work out the change in y from (0, 1) to (4, 9).

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Answer: 8

  1. Difference in y-coordinates: 9 - 1.
  2. Result is 8.
  • Method (1): Difference in y-coordinates: 9 - 1.
  • Accuracy (1): Result is 8.

Question 6 Hard

A line has gradient 5 and passes through (0, 2). Work out y when x=1.

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Answer: 7

  1. Equation: y = 5x + 2.
  2. When x = 1: y = 5(1) + 2 = 7.
  • Method (1): Equation: y = 5x + 2.
  • Accuracy (1): When x = 1: y = 5(1) + 2 = 7.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

A line has gradient 3 and passes through (0, 5). Work out y when x=4.

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Answer: 17

  1. Line formula is y = 3x + 5.
  2. Substitute x = 4: y = 3(4) + 5 = 12 + 5 = 17.
  • Method (1): y = 3x + 5, or 3 × 4 + 5
  • Accuracy (1): 17

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

What is the formula for the gradient m of a line through (x_A, y_A) and (x_B, y_B)?

  1. m = (y_B - y_A) / (x_B - x_A)
  2. m = (x_B - x_A) / (y_B - y_A)
  3. m = (y_B + y_A) / (x_B + x_A)
Show answer

m = (y_B - y_A) / (x_B - x_A) Gradient is vertical rise over horizontal run.

Check 2

What is the gradient of the line through (1, 2) and (5, 10)?

  1. 2
  2. 0.5
  3. 8
Show answer

2 (10 - 2) / (5 - 1) = 8 / 4 = 2.

Check 3

What is the gradient of the line through (0, 4) and (2, 0)?

  1. -2
  2. 2
  3. -0.5
Show answer

-2 (0 - 4) / (2 - 0) = -4 / 2 = -2.

Check 4

If y increases as x increases, what is the sign of the gradient?

  1. Positive
  2. Negative
  3. Zero
Show answer

Positive Rising from left to right is positive gradient.

Check 5

If y decreases as x increases, what is the sign of the gradient?

  1. Negative
  2. Positive
  3. Undefined
Show answer

Negative Falling from left to right is negative gradient.

Check 6

What is the change in y from (1, 2) to (5, 10)?

  1. 8
  2. 4
  3. 2
Show answer

8 10 - 2 = 8.

Check 7

What is the change in y from (2, 6) to (5, 0)?

  1. -6
  2. 6
  3. -3
Show answer

-6 0 - 6 = -6.

Check 8

A line has gradient 3 and passes through (0, 1). What is y when x = 2?

  1. 7
  2. 6
  3. 5
Show answer

7 y = 3(2) + 1 = 7.

Check 9

A line has gradient 2 and passes through (0, 4). What is y when x = 3?

  1. 10
  2. 6
  3. 8
Show answer

10 y = 2(3) + 4 = 10.

Check 10

Why is gradient not equal to change in x divided by change in y?

  1. Gradient measures vertical rise per horizontal step
  2. Because x is always bigger
  3. Because y comes first alphabetically
Show answer

Gradient measures vertical rise per horizontal step By definition, slope is vertical change divided by horizontal change.

Check 11

In y = mx + c, which letter represents the gradient?

  1. m
  2. c
  3. x
Show answer

m m is the multiplier of x (the gradient).

Check 12

What is the gradient of the line through (2, 3) and (5, 12)?

  1. 3
  2. 9
  3. 4
Show answer

3 (12 - 3) / (5 - 2) = 9 / 3 = 3.

Check 13

A line has gradient 4 and passes through (0, 1). What is y when x = 2?

  1. 9
  2. 8
  3. 7
Show answer

9 y = 4(2) + 1 = 9.

Check 14

What is the gradient of a horizontal line?

  1. 0
  2. 1
  3. Undefined
Show answer

0 There is zero vertical change (dy = 0).

Check 15

What is the gradient of the line through (0, 1) and (3, 7)?

  1. 2
  2. 6
  3. 3
Show answer

2 (7 - 1) / (3 - 0) = 6 / 3 = 2.

Keep going with Gradient of a line

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