1.4 Lesson 3 Connecting One Variable Inequalites to Two Variable Inequalities

Open Ended

What do you notice about the y-coordinates when comparing X's and circles with the same x-coordinate on the grid?

Multiple Choice

What is the equation of the boundary line for the inequality y ≥ -1/4x + 2?

• y = -1/4x + 2

• y = 1/4x + 2

• y = -1/4x - 2

• y = 1/4x - 2

Multiple Select

Which of the following ordered pairs is a solution to the inequality y ≥ -1/4x + 2?

• (2,2)

• (2,0)

• (4,1)

• (0,0)

Multiple Choice

Which part of the graph corresponds to the mathematical statement y > -1/4x + 2?

• Boundary line

• Shaded region

• Both boundary line and shaded region

• Neither

Open Ended

How does the graph of y ≤ -1/4x + 2 look different from the graph of y ≥ -1/4x + 2?

Multiple Choice

What do you think a solid boundary line means on the graph of a linear inequality?

• Points on the line are in the solution set

• Points on the line are not in the solution set

• The line is only for reference

• The line is not part of the graph

Open Ended

Explain how the solid and dotted lines on the graphs of two-variable inequalities relate to closed and open circles on the graphs of one-variable inequalities.

Multiple Choice

Which of the following statements about the graphical representation of linear inequalities is correct?

• A dotted boundary line means points on the line are not included in the solution set.

• A solid boundary line means points on the line are not included in the solution set.

• A solid boundary line means points on the line are excluded from the solution set.

• A dotted boundary line means points on the line are included in the solution set.

Multiple Choice

Which of the following inequalities would have a solid boundary line when graphed?

• y ≥ 2x + 1

• y < -x + 3

• y > 4x - 5

• y < 2x - 7

Multiple Choice

What does the shaded region on the graph of a linear inequality in two variables represent?

• All possible values of x and y

• The solution set of the inequality

• The boundary line only

• The x-intercepts

Open Ended

Explain why the point (2, -5) is not part of the solution set for the inequality y > -3x + 1, even though it is on the boundary line.

Multiple Select

Select all the points that are solutions to the inequality y > -3x + 1.

• (2, 1)

• (2, -5)

• (2, 0)

• (2, -3)

Multiple Select

Select all statements that are true about the shaded regions in the graphs of x ≥ -2 and y < 3.

• The shaded region for x ≥ -2 is to the right of x = -2.

• The shaded region for y < 3 is below y = 3.

• Both shaded regions include the origin (0,0).

• The shaded region for x ≥ -2 is above the x-axis.

Multiple Choice

Which inequality matches the graph that is shaded to the right of the vertical line x = -1.5?

• x > -1.5

• x < -1.5

• y > -1.5

• y < -1.5

Open Ended

All of the graphs have dashed lines. The x graphs are vertical lines. Each graph is shaded a different direction. The y graphs are horizontal lines. What do you notice and wonder about these graphs?