Question 1

Which of the following is the correct first step when graphing the linear inequality $$2x - 3y \u003c 6$$?

Accepted Answer

Graph the boundary line $$2x - 3y = 6$$ using a dashed line.

Question 2

Given the inequality $$y \geq -2x + 1$$, which of the following statements is TRUE about its graph?

Accepted Answer

The boundary line is solid and the region above the line is shaded.

Question 3

If the test point $$(0,0) is $$used for the inequality $$x - y \u003e 3$$ and it results in a false statement, what should you do next?

Accepted Answer

Shade the half-plane that does not contain $$(0,0).$$

Question 4

Which of the following ordered pairs is a solution to the inequality $$y \u003c 2x - 1$$?

Accepted Answer

$$(2, 0)$$

Question 5

A company wants to model the constraint that the number of products $$x$$ and $$y$$ they produce must satisfy $$3x + 2y \leq 12. $$Which of the following best describes the region representing all possible solutions?

Accepted Answer

The region below the line $$3x + 2y = 12$$, including the line.

Question 6

Which of the following inequalities would have a boundary line that passes through $$(0,0)$$ and is shaded above the line?

Accepted Answer

$$y \u003e x$$

Question 7

When graphing the intersection of $$y \u003e x$$ and $$y \u003c -x + 4$$, what region is shaded?

Accepted Answer

The region between the two lines.

Question 8

Suppose you are graphing $$x + y \leq 5$$ and $$x - y \geq 1. $$What is the solution set?

Accepted Answer

The region where the two shaded areas overlap.

Question 9

Which of the following is NOT a correct step when graphing a linear inequality?

Accepted Answer

Always use $$(0,0) as $$the test point, even if it lies on the boundary line.

Question 10

A medical researcher is modeling a safe dosage region for a drug using $$x + 2y  0. $$Which region represents all possible safe dosages?

Accepted Answer

The region to the right of $$x = 0$$ and below $$x + 2y = 10.$$

Question 11

If the boundary line for an inequality is $$y = -\frac{1}{2}x + 3$$ and the inequality is $$y \leq -\frac{1}{2}x + 3$$, which of the following is true?

Accepted Answer

The boundary line is solid and the region below the line is shaded.

Question 12

Which of the following best describes the union of the solution sets for $$y \u003e 2x - 1$$ and $$y \u003c -x + 4$$?

Accepted Answer

The region where at least one of the inequalities is true.

Question 13

A business constraint is modeled by $$x \geq 0$$ and $$y \geq 0. $$What does the solution set represent?

Accepted Answer

All points in the first quadrant.

Question 14

Which of the following is a correct interpretation of the shaded region for $$y \u003c 3x + 2$$?

Accepted Answer

All points below the line $$y = 3x + 2.$$

Question 15

If you are graphing $$2x - y \geq 4$$ and the test point $$(0,0)$$ gives a false statement, which region do you shade?

Accepted Answer

The region not containing $$(0,0).$$

Question 16

Which of the following is a solution to both $$y \u003e x$$ and $$y \u003c 2x$$?

Accepted Answer

$$(1, 1.5)$$

Question 17

A region is defined by $$x + y \u003e 2$$ and $$x - y \u003c 4. $$Which of the following points is in the intersection of the two regions?

Accepted Answer

$$(2, 1)$$

Question 18

Which of the following best describes the process for graphing $$y \u003c -x + 5$$?

Accepted Answer

Graph the line $$y = -x + 5$$ with a dashed line and shade below.

Question 19

If the boundary line for an inequality passes through $$(0,0)$$, what should you do when choosing a test point?

Accepted Answer

Choose a point not on the boundary line.

Graphing Linear Inequalities and Their Intersections in Two Variables

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