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Inequalities on graphs practice questions with answers

Higher · Grade 6 · Non-calculator

A second set of inequalities on graphs 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.

More questions

Question 1 Easy

Is the point (2, 5) above, below or on the line y=2x+1?

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Answer: on the line

  1. Line at x=2 is y=5.
  2. Point y = 5 matches line, so on the line.
  • Method (1): Line at x=2 is y=5.
  • Accuracy (1): Point y = 5 matches line, so on the line.

Question 2 Easy

Is the point (1, 0) above, below or on the line y=3x+2?

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Answer: below

  1. Line at x=1 is y=5.
  2. 0 < 5, so the point is below.
  • Method (1): Line at x=1 is y=5.
  • Accuracy (1): 0 < 5, so the point is below.

Question 3 Medium

Does the point (5, 3) satisfy the inequality y<x?

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Answer: yes

  1. Test 3 < 5: true.
  2. Answer yes.
  • Method (1): Test 3 < 5: true.
  • Accuracy (1): Answer yes.

Question 4 Medium

Does the point (0, 1) satisfy the inequality y<x?

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Answer: no

  1. Test 1 < 0: false.
  2. Answer no.
  • Method (1): Test 1 < 0: false.
  • Accuracy (1): Answer no.

Question 5 Hard

Find the gradient of the boundary line y=2x.

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Answer: 2

  1. Read coefficient of x.
  2. Gradient is 2.
  • Method (1): Read coefficient of x.
  • Accuracy (1): Gradient is 2.

Question 6 Hard

Find the gradient of the boundary line y=-3x.

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Answer: -3

  1. Read coefficient of x.
  2. Gradient is -3.
  • Method (1): Read coefficient of x.
  • Accuracy (1): Gradient is -3.

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

Is the point (2, 7) above, below or on the line y=3x-1?

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Answer: above

  1. Substitute x = 2 into the line equation: y = 3(2) - 1 = 5.
  2. The point has y = 7, and 7 > 5, so the point is above the line.
  • Method (1): Finds the line value 5 at x = 2
  • Accuracy (1): Conclusion above

Quick checks

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

Check 1

A point with a higher y than the line at that x is

  1. above the line
  2. intercept is -4
  3. gradient is 2
Show answer

above the line Above the line.

Check 2

Point (1, 5) and the line y=2x+1 sits

  1. below the line
  2. on the line
  3. above the line
Show answer

above the line Above, because the line is only at 3.

Check 3

Point (3, 2) and the line y=x+4 sits

  1. below the line
  2. above the line
  3. on the line
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below the line Below, because the line is at 7.

Check 4

Point (2, 5) and the line y=2x+1 sits

  1. on the line
  2. below the line
  3. above the line
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on the line On the line.

Check 5

Does (4, 1) satisfy y<x?

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Yes, 1 < 4. Yes, 1 < 4.

Check 6

Does (1, 4) satisfy y<x?

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No, 4 is not less than 1. No, 4 is not less than 1.

Check 7

Equal coordinates and a strict inequality: (2, 2) with y<x gives

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No, because equal is not less than. No, because equal is not less than.

Check 8

Intercept of the boundary y=2x+1 is

  1. gradient is 2
  2. gradient is -3
  3. intercept is 1
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intercept is 1 1.

Check 9

Intercept of the boundary y=3x-4 is

  1. gradient is 5
  2. gradient is -3
  3. intercept is -4
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intercept is -4 -4.

Check 10

Slope of the boundary line y=2x is

  1. above the line
  2. gradient is 2
  3. intercept is 1
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gradient is 2 2.

Check 11

Slope of the boundary line y=5x is

  1. gradient is 2
  2. gradient is 5
  3. intercept is 1
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gradient is 5 5.

Check 12

Downhill boundary: the gradient of the boundary line y=-3x is

  1. gradient is -3
  2. gradient is 5
  3. intercept is -4
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gradient is -3 -3.

Check 13

Why compare the point with the line’s y, not with zero?

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Above and below are about the line, not the x-axis. Above and below are about the line, not the x-axis.

Check 14

A boundary’s constant term tells you the

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y-intercept. y-intercept.

Check 15

A boundary’s number in front of x tells you the

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Gradient. Gradient.

Keep going with Inequalities on graphs

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