Worksheet: Two-Variable Linear Inequalities

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?

  • A𝑦4𝑥3
  • B𝑦>4𝑥3
  • C𝑦<3𝑥+4
  • D𝑦3𝑥+4
  • E𝑦<4𝑥3

Q3:

What is the inequality graphed in the given figure?

  • A𝑦>2
  • B𝑦<2
  • C𝑦0
  • D𝑦2
  • E𝑦2

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
  • B𝑦3𝑥2
  • C𝑦<3𝑥2
  • D𝑦2𝑥+3
  • E𝑦>3𝑥2

Q6:

Which inequality has been graphed in the given figure?

  • A𝑦<2𝑥+4
  • B𝑦>2𝑥+4
  • C𝑦<4𝑥2
  • D𝑦2𝑥+4
  • E𝑦4𝑥2

Q7:

Which inequality has been graphed in the given figure?

  • A𝑦2𝑥+4
  • B𝑦4𝑥2
  • C𝑦4𝑥2
  • D𝑦>4𝑥2
  • E𝑦<2𝑥+4

Q8:

Which of the following figures is the correct graph of 𝑦𝑥?

  • A
  • B
  • C
  • D
  • E

Q9:

What is the inequality graphed in the given figure?

  • A𝑦0
  • B𝑦<2
  • C𝑦>2
  • D𝑦2
  • E𝑦2

Q10:

Which inequality has been graphed in the given figure?

  • A𝑦2𝑥4
  • B𝑦4𝑥+2
  • C𝑦<2𝑥4
  • D𝑦>2𝑥4
  • 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 𝑦𝑥?

  • A
  • B
  • C
  • D
  • E

Q13:

Which inequality has been graphed in the given figure?

  • A𝑦<2𝑥13
  • B𝑦13𝑥2
  • C𝑦2𝑥13
  • D𝑦>13𝑥2
  • E𝑦<13𝑥2

Q14:

Which inequality has been graphed in the given figure?

  • A𝑦>5𝑥+5
  • B𝑦5𝑥+5
  • C𝑦5𝑥5
  • D𝑦5𝑥5
  • E𝑦<5𝑥5

Q15:

Which inequality has been graphed in the given figure?

  • A𝑦4𝑥+3
  • B𝑦4𝑥+3
  • C𝑦<3𝑥4
  • D𝑦3𝑥4
  • E𝑦>4𝑥+3

Q16:

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

  • A2𝑦3𝑥<3
  • B2𝑦+3𝑥3
  • C2𝑦3𝑥3
  • D2𝑦3𝑥>3
  • E2𝑦3𝑥>3

Q17:

Which inequality has been graphed in the given figure?

  • A𝑦15𝑥3
  • B𝑦<15𝑥3
  • C𝑦>3𝑥15
  • D𝑦3𝑥15
  • E𝑦15𝑥3

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 𝑦𝑥.
  • BFigure 1 shows 𝑦𝑥, figure 2 shows 𝑦>𝑥.

Q19:

Which inequality has been graphed in the given figure?

  • A𝑦14𝑥+3
  • B𝑦>14𝑥+3
  • C𝑦<3𝑥14
  • D𝑦14𝑥+3
  • E𝑦3𝑥14

Q20:

Write the inequality represented by the coloured region.

  • A𝑦>3𝑥5
  • B𝑦3𝑥5
  • C𝑦<3𝑥+5
  • D𝑦3𝑥+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
  • B10.5𝑥15𝑦<41
  • C10.5𝑥+15𝑦=41
  • D10.5𝑥+15𝑦41
  • E10.5𝑥+15𝑦>41

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