Lesson Worksheet: Two-Variable Linear Inequalities Mathematics

In this worksheet, we will practice graphing two-variable linear inequalities.

Q1:

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

  • A
  • B
  • C
  • D
  • E

Q2:

Which inequality has been graphed in the given figure?

  • A𝑦≥4𝑥−3
  • B𝑦>4𝑥−3
  • C𝑦<−3𝑥+4
  • D𝑦≤−3𝑥+4
  • E𝑦<4𝑥−3

Q3:

What is the inequality graphed in the given figure?

  • A𝑦>2
  • B𝑦<2
  • C𝑦≤0
  • D𝑦≥2
  • E𝑦≤2

Q4:

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

  • A
  • B
  • C
  • D
  • E

Q5:

Which inequality has been graphed in the given figure?

  • A𝑦<−2𝑥+3
  • B𝑦≥3𝑥−2
  • C𝑦<3𝑥−2
  • D𝑦≤−2𝑥+3
  • E𝑦>3𝑥−2

Q6:

Which inequality has been graphed in the given figure?

  • A𝑦<−2𝑥+4
  • B𝑦>−2𝑥+4
  • C𝑦<4𝑥−2
  • D𝑦≤−2𝑥+4
  • E𝑦≥4𝑥−2

Q7:

Which inequality has been graphed in the given figure?

  • A𝑦≥−2𝑥+4
  • B𝑦≤4𝑥−2
  • C𝑦≥4𝑥−2
  • D𝑦>4𝑥−2
  • E𝑦<−2𝑥+4

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

What is the inequality graphed in the given figure?

  • A𝑦≥0
  • B𝑦<2
  • C𝑦>2
  • D𝑦≤2
  • E𝑦≥2

Q10:

Which inequality has been graphed in the given figure?

  • A𝑦≥2𝑥−4
  • B𝑦≤−4𝑥+2
  • C𝑦<2𝑥−4
  • D𝑦>2𝑥−4
  • E𝑦>−4𝑥+2

Q11:

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

  • A
  • B
  • C
  • D
  • E

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?

  • A𝑦<−2𝑥−13
  • B𝑦≤−13𝑥−2
  • C𝑦≥−2𝑥−13
  • D𝑦>−13𝑥−2
  • E𝑦<−13𝑥−2

Q14:

Which inequality has been graphed in the given figure?

  • A𝑦>−5𝑥+5
  • B𝑦≤−5𝑥+5
  • C𝑦≤5𝑥−5
  • D𝑦≥5𝑥−5
  • E𝑦<5𝑥−5

Q15:

Which inequality has been graphed in the given figure?

  • A𝑦≥−4𝑥+3
  • B𝑦≤−4𝑥+3
  • C𝑦<3𝑥−4
  • D𝑦≤3𝑥−4
  • E𝑦>−4𝑥+3

Q16:

Determine the inequality whose solution set is represented by the colored region.

  • A2𝑦−3𝑥<−3
  • B2𝑦+3𝑥≤−3
  • C2𝑦−3𝑥≥3
  • D2𝑦−3𝑥>−3
  • E2𝑦−3𝑥>3

Q17:

Which inequality has been graphed in the given figure?

  • A𝑦≤−15𝑥−3
  • B𝑦<−15𝑥−3
  • C𝑦>−3𝑥−15
  • D𝑦≥−3𝑥−15
  • E𝑦≥−15𝑥−3

Q18:

Consider the inequalities shown in figure 1 and figure 2.

Which of the following is correct?

  • AFigure 1 shows 𝑦>𝑥, figure 2 shows 𝑦≥𝑥.
  • BFigure 1 shows 𝑦≥𝑥, figure 2 shows 𝑦>𝑥.

Q19:

Which inequality has been graphed in the given figure?

  • A𝑦≤−14𝑥+3
  • B𝑦>−14𝑥+3
  • C𝑦<3𝑥−14
  • D𝑦≥−14𝑥+3
  • E𝑦≥3𝑥−14

Q20:

Write the inequality represented by the coloured region.

  • A𝑦>3𝑥−5
  • B𝑦≥3𝑥−5
  • C𝑦<3𝑥+5
  • D𝑦≤−3𝑥+5
  • E𝑦>3𝑥+5

Q21:

A library offers two types of notebooks; the price of the first is 10.5 LE and the second is 15 LE. If David does not want to spend more than 41 LE, express a relation that shows how many notebooks he can buy.

  • A10.5𝑥+15𝑦<41
  • B10.5𝑥−15𝑦<41
  • C10.5𝑥+15𝑦=41
  • D10.5𝑥+15𝑦≤41
  • E10.5𝑥+15𝑦>41

Q22:

True or False: The graph shown represents the inequality 𝑦≤12𝑥−6.

  • AFalse
  • BTrue

Q23:

Write down the inequality represented in the graph shown.

  • A𝑦<𝑥
  • B𝑦=𝑥
  • C𝑦>𝑥
  • D𝑦≥𝑥
  • E𝑦≤𝑥

Q24:

Which of the following figures is the correct graph of 𝑦<𝑥+1?

  • A
  • B
  • C
  • D
  • E

Q25:

What is the inequality graphed in the given figure?

  • A𝑦≤𝑥+1
  • B𝑦=𝑥+1
  • C𝑦>𝑥+1
  • D𝑦≥𝑥+1
  • E𝑦<𝑥+1

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