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

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>π‘₯, figure 2 shows 𝑦β‰₯π‘₯.
  • BFigure 1 shows 𝑦β‰₯π‘₯, figure 2 shows 𝑦>π‘₯.

Q2:

Which inequality has been graphed in the given figure?

  • A𝑦β‰₯βˆ’2π‘₯+4
  • B𝑦≀4π‘₯βˆ’2
  • C𝑦β‰₯4π‘₯βˆ’2
  • D𝑦>4π‘₯βˆ’2
  • E𝑦<βˆ’2π‘₯+4

Q3:

Which inequality has been graphed in the given figure?

  • Aπ‘¦β‰€βˆ’15π‘₯βˆ’3
  • B𝑦<βˆ’15π‘₯βˆ’3
  • C𝑦>βˆ’3π‘₯βˆ’15
  • D𝑦β‰₯βˆ’3π‘₯βˆ’15
  • E𝑦β‰₯βˆ’15π‘₯βˆ’3

Q4:

Which of the following figures is the correct graph of 𝑦<π‘₯?

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following figures is the correct graph of 𝑦=π‘₯?

  • A
  • B
  • C
  • D
  • E

Q6:

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

  • A2π‘¦βˆ’3π‘₯<βˆ’3
  • B2𝑦+3π‘₯β‰€βˆ’3
  • C2π‘¦βˆ’3π‘₯β‰₯3
  • D2π‘¦βˆ’3π‘₯>βˆ’3
  • E2π‘¦βˆ’3π‘₯>3

Q7:

Which inequality has been graphed in the given figure?

  • A𝑦<βˆ’2π‘₯βˆ’13
  • Bπ‘¦β‰€βˆ’13π‘₯βˆ’2
  • C𝑦β‰₯βˆ’2π‘₯βˆ’13
  • D𝑦>βˆ’13π‘₯βˆ’2
  • E𝑦<βˆ’13π‘₯βˆ’2

Q8:

True or False: The graph shown represents the inequality 𝑦≀12π‘₯βˆ’6.

  • AFalse
  • BTrue

Q9:

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

  • A𝑦β‰₯4π‘₯βˆ’3
  • B𝑦>4π‘₯βˆ’3
  • C𝑦<βˆ’3π‘₯+4
  • Dπ‘¦β‰€βˆ’3π‘₯+4
  • E𝑦<4π‘₯βˆ’3

Q10:

Fill in the blank: The point (4,βˆ’2) belongs to the solution set of the inequality 3π‘₯+2𝑦8.

  • A≀
  • Bβ‰ 
  • C>
  • D<

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