Graphing Systems of Linear Inequalities

The video tutorial explains how to graph a system of inequalities, specifically y > x - 8 and y < 5 - x. It demonstrates how to draw the boundary lines for each inequality, using dotted lines to indicate that the boundary is not included in the solution set. The tutorial then shows how to identify the region where the two inequalities overlap, which represents the solution set. The video emphasizes testing points to verify which regions satisfy the inequalities.

What is the y-intercept of the line represented by the equation y = x - 8?

• -1

• -8

• 8

• 0

What type of line is used to represent the inequality y > x - 8?

• Solid line

• Dotted line

• Dashed line

• Thick line

If the point (0, 0) is tested for the inequality y > x - 8, is it part of the solution set?

• Irrelevant to the inequality

• Cannot determine

• No

• Yes

What does the point (10, 0) tell us when tested against the inequality y > x - 8?

• It is an irrelevant point

• It is on the boundary line

• It is not part of the solution set

• It is part of the solution set

What is the slope of the line y = 5 - x?

• 1

• -1

• 0

• 5

Which type of line is used to graph the inequality y < 5 - x?

• Dashed line

• Dotted line

• Thick line

• Solid line

What is the y-intercept of the line represented by the equation y = 5 - x?

• -5

• 5

• 1

• 0

Does the point (0, 0) satisfy the inequality y < 5 - x?

• Yes

• No

• Irrelevant to the inequality

• Cannot determine

Where is the solution set for the system of inequalities located?

• Below both boundary lines

• Outside the boundary lines

• Above both boundary lines

• Between the boundary lines

Which region does the inequality y < 5 - x define?

• Above the line

• Below the line

• None of the above

• On the line