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Worksheet: Graphing Two-Variable Inequalities

In this worksheet, we will practice recognizing the inequalities represented on a graph.

Q1:

Which of the following figures is the correct graph of 𝑦 = 𝑥 ?

  • A
  • B
  • C
  • D
  • E

Q2:

What is the inequality graphed in the given figure?

  • A 𝑦 > 2
  • B 𝑦 ≤ 2
  • C 𝑦 < 2
  • D 𝑦 ≥ 2
  • E 𝑦 ≤ 0

Q3:

Which inequality has been graphed in the given figure?

  • A 𝑦 ≥ 4 𝑥 − 3
  • B 𝑦 > 4 𝑥 − 3
  • C 𝑦 ≤ − 3 𝑥 + 4
  • D 𝑦 < 4 𝑥 − 3
  • E 𝑦 < − 3 𝑥 + 4

Q4:

Which inequality has been graphed in the given figure?

  • A 𝑦 ≤ − 2 𝑥 + 4
  • B 𝑦 > − 2 𝑥 + 4
  • C 𝑦 ≥ 4 𝑥 − 2
  • D 𝑦 < − 2 𝑥 + 4
  • E 𝑦 < 4 𝑥 − 2

Q5:

Which inequality has been graphed in the given figure?

  • A 𝑦 ≥ 3 𝑥 − 2
  • B 𝑦 < 3 𝑥 − 2
  • C 𝑦 ≤ − 2 𝑥 + 3
  • D 𝑦 > 3 𝑥 − 2
  • E 𝑦 < − 2 𝑥 + 3

Q6:

Which region on the graph contains solutions to the set of inequalities

  • A B
  • B F
  • C A
  • D E
  • E C

Q7:

Which of the following figures is the correct graph of 𝑦 < 𝑥 ?

  • A
  • B
  • C
  • D
  • E

Q8:

Which inequality has been graphed in the given figure?

  • A 𝑦 > 4 𝑥 − 2
  • B 𝑦 ≤ 4 𝑥 − 2
  • C 𝑦 ≥ − 2 𝑥 + 4
  • D 𝑦 ≥ 4 𝑥 − 2
  • E 𝑦 < − 2 𝑥 + 4

Q9:

Which of the following figures is the correct graph of 𝑦 ≤ 𝑥 ?

  • A
  • B
  • C
  • D
  • E

Q10:

Which inequality has been graphed in the given figure?

  • A 𝑦 ≤ − 1 3 𝑥 − 2
  • B 𝑦 > − 1 3 𝑥 − 2
  • C 𝑦 < − 2 𝑥 − 1 3
  • D 𝑦 < − 1 3 𝑥 − 2
  • E 𝑦 ≥ − 2 𝑥 − 1 3

Q11:

Which region on the graph contains solutions to the set of inequalities

  • A A
  • B C
  • C D
  • D E
  • E F

Q12:

Which of the following figures is the correct graph of 𝑦 > 𝑥 ?

  • A
  • B
  • C
  • D
  • E

Q13:

Which inequality has been graphed in the given figure?

  • A 𝑦 < 5 𝑥 − 5
  • B 𝑦 ≥ 5 𝑥 − 5
  • C 𝑦 > − 5 𝑥 + 5
  • D 𝑦 ≤ 5 𝑥 − 5
  • E 𝑦 ≤ − 5 𝑥 + 5

Q14:

Which inequality has been graphed in the given figure?

  • A 𝑦 ≥ 3 𝑥 − 1 4
  • B 𝑦 ≤ − 1 4 𝑥 + 3
  • C 𝑦 > − 1 4 𝑥 + 3
  • D 𝑦 ≥ − 1 4 𝑥 + 3
  • E 𝑦 < 3 𝑥 − 1 4

Q15:

Which region on the graph contains solutions to the set of inequalities