Inequalities and Their Graphs

This lesson covers graphing inequalities in two variables, focusing on understanding boundaries, half-planes, and the process of graphing linear inequalities. It includes testing points and shading regions to determine solution sets. The lesson provides examples and applies these concepts to a real-world scenario involving a work schedule.

What is a boundary in the context of graphing inequalities?

• A line that divides the coordinate plane into two half-planes

• A circle that represents the solution set

• A point where two lines intersect

• A region where all solutions of an inequality lie

When graphing an inequality, when do you use a dashed line?

• When the inequality is greater than or less than

• When the inequality is greater than or equal to

• When the inequality is equal to

• When the inequality is less than or equal to

What is the first step in graphing the inequality 2y - 4x > 6?

• Shade the region

• Graph the line y = 2x + 3

• Solve for y

• Test a point

In the inequality 2y - 4x > 6, what is the slope of the line y = 2x + 3?

• -1/2

• 1/2

• -2

• 2

What point is commonly used to test which side of the line to shade?

• (-1, -1)

• (2, 2)

• (1, 1)

• (0, 0)

In the inequality y - 3x < 2, what is the y-intercept of the line y = 3x + 2?

• -3

• 2

• 3

• -2

For the inequality y - 3x < 2, what type of line is used to graph it?

• Dashed line

• Solid line

• Thick line

• Dotted line

In the inequality x + 4y ≥ 2, what is the slope of the line y = -1/4x + 1/2?

• -1/4

• 1/4

• 2

• -2

What does the inequality symbol '≥' indicate about the line type?

• No line

• Dotted line

• Solid line

• Dashed line

In the inequality x + 2y ≥ 6, which graphs can be eliminated immediately?

• Graphs with solid lines

• Graphs with dotted lines

• Graphs with no lines

• Graphs with dashed lines