Graphing Inequalities and Test Points

The video tutorial explains how to graph the inequality y ≥ -2/3x + 4. It covers the steps to graph the line using the slope-intercept form, determining whether the line should be solid or dashed based on the inequality symbol, and shading the correct region of the graph. The tutorial also includes verifying the solution by testing points in the shaded and non-shaded regions. It concludes with recommendations for graphing inequalities effectively.

What is the first step in graphing the inequality y ≥ -2/3x + 4?

• Shade the region above the line

• Plot the y-intercept and use the slope

• Draw a dashed line

• Test a point in the region

When should you use a solid line while graphing an inequality?

• When the inequality is strict (< or >)

• When the y-intercept is zero

• When the inequality includes equality (≤ or ≥)

• When the slope is positive

How do you determine additional points on the line y = -2/3x + 4?

• By using the x-intercept

• By testing random points

• By using the slope to move from the y-intercept

• By drawing a horizontal line

What does the slope -2/3 represent in the equation y = -2/3x + 4?

• The x-intercept

• The y-intercept

• The change in y for a unit change in x

• The change in x for a unit change in y

What is the y-intercept of the line y = -2/3x + 4?

• 0

• 4

• -2/3

• 3

Which region should be shaded for the inequality y ≥ -2/3x + 4?

• Below the line

• Above the line

• On the line

• To the left of the line

What is the purpose of testing points when graphing inequalities?

• To verify the correct region is shaded

• To find the slope

• To calculate the x-intercept

• To determine the y-intercept

Why is it important to verify the shaded region with test points?

• To determine the slope

• To find the exact solution

• To confirm the correct side of the line is shaded

• To ensure the line is drawn correctly

Which point is used to verify the shaded region in the video?

• (2,2)

• (1,1)

• (3,3)

• (0,0)

What is the result of substituting (0,0) into the inequality y ≥ -2/3x + 4?

• 0 ≥ 4, which is true

• 0 ≤ 4, which is false

• 0 ≥ 4, which is false

• 0 ≤ 4, which is true