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Equation of a line practice questions with answers

Foundation and Higher · Grade 5 · Non-calculator

A second set of equation 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

Write down the equation of the line with gradient 6 and y-intercept 1.

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Answer: y=6x+1

  1. Gradient multiplies x: 6x.
  2. Intercept is added: y = 6x + 1.
  • Method (1): Gradient multiplies x: 6x.
  • Accuracy (1): Intercept is added: y = 6x + 1.

Question 2 Easy

Write down the equation of the line with gradient 2 and y-intercept -5.

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Answer: y=2x-5

  1. Gradient multiplies x: 2x.
  2. Intercept is subtracted: y = 2x - 5.
  • Method (1): Gradient multiplies x: 2x.
  • Accuracy (1): Intercept is subtracted: y = 2x - 5.

Question 3 Medium

Write down the equation of the line through (0, 6) with gradient 2.

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Answer: y=2x+6

  1. Point (0, 6) means intercept c = 6.
  2. Gradient m = 2 gives y = 2x + 6.
  • Method (1): Point (0, 6) means intercept c = 6.
  • Accuracy (1): Gradient m = 2 gives y = 2x + 6.

Question 4 Medium

Write down the equation of the line through (0, -1) with gradient 5.

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Answer: y=5x-1

  1. Point (0, -1) means intercept c = -1.
  2. Gradient m = 5 gives y = 5x - 1.
  • Method (1): Point (0, -1) means intercept c = -1.
  • Accuracy (1): Gradient m = 5 gives y = 5x - 1.

Question 5 Hard

Write down the y-intercept of the line y=3x-4.

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Answer: -4

  1. Read the constant term with its sign.
  2. Constant is -4.
  • Method (1): Read the constant term with its sign.
  • Accuracy (1): Constant is -4.

Question 6 Hard

Write down the y-intercept of the line y=4x+7.

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Answer: 7

  1. Read the constant term.
  2. Constant is 7.
  • Method (1): Read the constant term.
  • Accuracy (1): Constant is 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

Write down the gradient and the y-intercept of the line y=-3x+8.

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Answer: -3 and 8

  1. In y = mx + c, the gradient m is the coefficient of x, so m = -3.
  2. The y-intercept c is the constant term, so c = 8.
  • Mark (1): Gradient -3
  • Mark (1): y-intercept 8

Quick checks

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

Check 1

In the equation y = mx + c, what does m represent?

  1. The gradient of the line
  2. The y-intercept
  3. The x-intercept
Show answer

The gradient of the line m is the gradient (slope).

Check 2

In the equation y = mx + c, what does c represent?

  1. The y-intercept
  2. The gradient
  3. The length of the line
Show answer

The y-intercept c is where the line crosses the y-axis at (0, c).

Check 3

What is the equation of the line with gradient 2 and intercept 1?

  1. y=2x+1
  2. y=x+2
  3. y=2x-1
Show answer

y=2x+1 m = 2 and c = 1 gives y = 2x + 1.

Check 4

What is the equation of the line with gradient 3 and intercept -4?

  1. y=3x-4
  2. y=4x-3
  3. y=3x+4
Show answer

y=3x-4 m = 3 and c = -4 gives y = 3x - 4.

Check 5

What is the equation of the line through (0, 1) with gradient 4?

  1. y=4x+1
  2. y=x+4
  3. y=4x-1
Show answer

y=4x+1 Crossing at (0, 1) means c = 1, so y = 4x + 1.

Check 6

What is the equation of the line through (0, -2) with gradient 3?

  1. y=3x-2
  2. y=2x-3
  3. y=3x+2
Show answer

y=3x-2 c = -2 and m = 3 gives y = 3x - 2.

Check 7

What is the gradient of the line y = 5x - 1?

  1. 5
  2. -1
  3. 4
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5 The coefficient of x is 5.

Check 8

What is the gradient of the line y = -2x + 3?

  1. -2
  2. 3
  3. 2
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-2 The coefficient of x is -2.

Check 9

What is the y-intercept of the line y = 3x - 4?

  1. -4
  2. 3
  3. 4
Show answer

-4 The constant term is -4.

Check 10

What is the y-intercept of the line y = 4x + 7?

  1. 7
  2. 4
  3. -7
Show answer

7 The constant term is +7.

Check 11

What is the equation of the line with gradient 5 and intercept 2?

  1. y=5x+2
  2. y=2x+5
  3. y=5x-2
Show answer

y=5x+2 y = mx + c = 5x + 2.

Check 12

What is the equation of the line through (0, 6) with gradient 2?

  1. y=2x+6
  2. y=6x+2
  3. y=2x-6
Show answer

y=2x+6 Point (0, 6) gives c = 6, so y = 2x + 6.

Check 13

Why is the gradient not the standalone number?

  1. The gradient is a rate that multiplies x
  2. Because the standalone number is bigger
  3. It is an arbitrary rule
Show answer

The gradient is a rate that multiplies x As x changes, mx changes proportional to m.

Check 14

At what coordinate does the line y = 2x - 5 cross the y-axis?

  1. (0, -5)
  2. (-5, 0)
  3. (0, 2)
Show answer

(0, -5) When x = 0, y = -5.

Check 15

What is the gradient of the line y = x + 3?

  1. 1
  2. 3
  3. 0
Show answer

1 When no number is shown in front of x, the coefficient is 1.

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