Graphing Systems of Inequalities Mastery

This video tutorial covers graphing systems of inequalities, starting with an introduction to the concept and moving through specific examples. It explains how to graph inequalities on a coordinate plane, including both dotted and solid lines, and how to determine the solution region by identifying overlapping shaded areas. The tutorial also demonstrates how to write inequalities from given graphs and apply these skills to solve real-world problems, such as time management scenarios.

What does a dotted line represent when graphing an inequality?

• The inequality is always less than.

• The inequality is always greater than.

• The inequality does not include the boundary line.

• The inequality includes the boundary line.

When graphing the inequality y > -2x + 2, where do you start on the y-axis?

• At y = -2

• At y = 2

• At y = -1

• At y = 1

For the inequality y < 2x - 3, what is the slope of the line?

• -2

• 2

• -1/2

• 1/2

If an inequality has a 'greater than or equal to' symbol, what type of line should be used?

• Solid line

• Dotted line

• Dashed line

• No line

When shading the region for y > 3x - 4, which side of the line do you shade?

• Below the line

• To the right of the line

• To the left of the line

• Above the line

What is the y-intercept of the line y = -1/2x + 5?

• 1/2

• -1/2

• -5

• 5

How do you determine the slope of a line from a graph?

• By finding the y-intercept

• By counting the rise over run between two points

• By measuring the angle of the line

• By looking at the x-intercept

In the context of inequalities, what does 'at most' mean?

• Greater than or equal to

• Less than

• Greater than

• Less than or equal to

If you can spend at least 1.5 hours on homework, how would you write this inequality?

• y ≥ 1.5

• y ≤ 1.5

• y > 1.5

• y < 1.5

What is the feasible region in a system of inequalities?

• The area to the left of all lines

• The area where all individual inequalities overlap

• The area above all lines

• The area below all lines