Determining Correct Shading of Half Planes on a Graph

The video tutorial explains how to determine if a half plane on a graph is correctly shaded by checking if a solution in the half plane makes the inequality true. It covers graphing inequalities, using points on the line, verifying shaded regions, and using the coordinate (0,0) for verification. The tutorial emphasizes that choosing a solution from the shaded region or using (0,0) can confirm correct shading.

What is the primary goal when determining if a half-plane is correctly shaded on a graph?

• To find the intersection of two lines

• To identify the midpoint of the line

• To ensure a solution in the half-plane makes the inequality true

• To calculate the slope of the line

When graphing the inequality Y ≤ X - 4, what type of line should be used to connect the points?

• A solid line

• A dotted line

• A dashed line

• No line is needed

Why is it not always sufficient to use a point on the line to verify correct shading of a half-plane?

• Points on the line are not part of the inequality

• Points on the line are always solutions

• Points on the line do not verify shading

• Points on the line are outside the region

What should you do to verify if the correct half-plane is shaded for the inequality Y > X - 8?

• Check a point on the line

• Check any point in the shaded region

• Check a point outside the shaded region

• Check the midpoint of the line

How can the coordinate (0,0) be used to verify the correct shading of a half-plane?

• By checking if it lies on the line

• By checking if it is in the shaded region and satisfies the inequality

• By checking if it is outside the graph

• By checking if it is the midpoint of the line

What conclusion can be drawn if (0,0) is not in the shaded region and does not satisfy the inequality?

• (0,0) is a solution

• (0,0) is not a solution

• (0,0) is the midpoint

• (0,0) is on the line

What is one method to ensure the correct half-plane is shaded?

• Check the slope of the line

• Use a point outside the graph

• Choose a solution from the shaded region

• Use the midpoint of the line