Graphing Inequalities and Shading Regions

The video tutorial explains how to graph the inequality y ≥ 2 on a coordinate plane. It begins by treating the inequality as a linear equation, y = 2, and discusses whether the line should be solid or dashed based on the inequality symbol. The tutorial clarifies the orientation of the line using a T table and demonstrates that y = 2 is a horizontal line. Finally, it shows how to determine which region to shade by interpreting the inequality, indicating that all points on the line and above it satisfy the inequality.

What is the first step in graphing the inequality y ≥ 2?

• Determine if the line is solid or dashed

• Plot the points (0, 2) and (3, 2)

• Graph the line y = 2

• Shade the region above the line

Why is the line y = 2 drawn as a solid line?

• Because it is a dashed line

• Because it is not part of the solution

• Because it is part of the solution

• Because it is a vertical line

What does the inequality symbol ≥ indicate about the line?

• The line should be vertical

• The line should be horizontal

• The line should be solid

• The line should be dashed

How can you determine if the line y = 2 is horizontal or vertical?

• By shading the region above the line

• By checking if x is present in the equation

• By plotting points using a T table

• By drawing a dashed line

Which points are used to sketch the line y = 2?

• (1, 2) and (2, 1)

• (2, 0) and (2, 3)

• (0, 2) and (3, 2)

• (0, 0) and (2, 2)

Where are the y-values greater than 2 located in relation to the line y = 2?

• To the left of the line

• Below the line

• Above the line

• On the line

What does shading the region above the line y = 2 represent?

• Points that are on the line

• Points that satisfy the inequality

• Points that are below the line

• Points that do not satisfy the inequality

What does the graph indicate about points in the shaded region?

• They are below the line

• They satisfy the inequality

• They are on the line

• They do not satisfy the inequality

What is true about points in the non-shaded region?

• They are above the line

• They are on the line

• They do not satisfy the inequality

• They satisfy the inequality

What is the inequality that points in the shaded region satisfy?

• y < 2

• y = 2

• y > 2

• y ≥ 2