Lesson Worksheet: Two-Variable Linear Inequalities Mathematics • 9th Grade

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

Q1:

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.

Q2:

Which inequality has been graphed in the given figure?

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

Q3:

Which inequality has been graphed in the given figure?

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

Q4:

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

  • A
  • B
  • C
  • D
  • E

Q5:

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

  • A
  • B
  • C
  • D
  • E

Q6:

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

Q7:

Which inequality has been graphed in the given figure?

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

Q8:

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

  • AFalse
  • BTrue

Q9:

Write the inequality that has been graphed in the given figure.

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

Q10:

Fill in the blank: The point (4,−2) belongs to the solution set of the inequality 3𝑥+2𝑦8.

  • A≤
  • B≠
  • C>
  • D<

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