Question 1

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

Accepted Answer

Solve the inequality for $$y in $$terms of $$x.$$

Question 2

When graphing the inequality $$y \u003c 2x + 1$$, how should the boundary line be drawn?

Accepted Answer

Dashed, because the points on the line are not included.

Question 3

Given the inequality $$x - 3 \u003c 1$$, what is the solution for $$x$$?

Accepted Answer

$$x \u003c 4$$

Question 4

For the inequality $$3x + 2y \geq 6$$, after solving for $$y$$, what is the slope of the boundary line?

Accepted Answer

$$-\frac{3}{2}$$

Question 5

If the inequality symbol is $$\leq or$$ $$\geq$$, how should the boundary line be drawn?

Accepted Answer

Solid

Question 6

When graphing $$y \u003e -x + 2$$, which region should be shaded?

Accepted Answer

Above the line

Question 7

A medical researcher is modeling a safe dosage region for a drug using the inequality $$2x + 5y \leq 20$$, where $$x$$ and $$y$$ are dosages of two chemicals. Which region represents safe dosages?

Accepted Answer

The region below and including the line $$2x + 5y = 20$$

Question 8

Which of the following points is a solution to the inequality $$3x + 2y \geq 6$$?

Accepted Answer

$$(3, 2)$$

Question 9

If you are graphing $$x \u003c 4$$, how should the boundary line be drawn and which side should be shaded?

Accepted Answer

Dashed line, shade to the left

Question 10

A company wants to keep the sum of two types of expenses, $$x$$ and $$y$$, at least $$1000. $$Which inequality represents this situation?

Accepted Answer

$$x + y \geq 1000$$

Question 11

Which of the following best describes the solution set for $$y \leq 2x - 5$$?

Accepted Answer

All points below and on the solid line $$y = 2x - 5$$

Question 12

If the inequality is $$y \u003e 3x - 2$$, which of the following is true about the boundary line and shading?

Accepted Answer

Dashed line, shade above

Question 13

A chemical reaction is safe if the temperature $$T$$ and pressure $$P$$ satisfy $$T + 2P \leq 100. $$Which of the following points is NOT in the safe region?

Accepted Answer

$$(50, 30)$$

Question 14

Which of the following is the correct way to check if a point is a solution to a linear inequality in two variables?

Accepted Answer

Substitute the point into the inequality and see if it makes the inequality true.

Question 15

For the inequality $$y \geq -\frac{1}{2}x + 3$$, which of the following statements is true?

Accepted Answer

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

Question 16

A city restricts water usage so that $$w \leq 5000$$ gallons per household per month. How should this be represented on a number line?

Accepted Answer

A solid point at 5000 with shading to the left

Question 17

Which of the following inequalities would have a solution set that includes the boundary line?

Accepted Answer

$$y \leq 2x + 1$$

Question 18

If you are given the inequality $$y \leq 4$$, what is the boundary line and which region is shaded?

Accepted Answer

Solid line at $$y = 4$$, shade below

Question 19

A business must keep the number of products $$p$$ produced each day at least 200. Which inequality models this situation?

Accepted Answer

$$p \geq 200$$

Graphing Linear Inequalities in Two Variables 2.4

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