Graphing Linear Inequalities Concepts

This video tutorial explains how to graph linear inequalities in two variables. It covers the steps to convert inequalities into equations, determine the type of line to draw (dashed or solid), and use test points to identify the solution region. Three examples are provided: graphing y < 5 - 3x, 3x - 2y ≥ 6, and y ≥ 2x, illustrating the process of plotting lines and shading solution areas.

What is the first step in graphing a linear inequality?

• Shade the region

• Select a test point

• Convert the inequality to an equation

• Determine the type of line

In Example 1, what type of line is used to graph y < 5 - 3x?

• Solid line

• Double line

• Dotted line

• Thick line

What is the slope of the line in the inequality y < 5 - 3x?

• 3

• 5

• -5

• -3

In Example 2, what is the vertical intercept of the line 3x - 2y = 6?

• (0, 3)

• (0, -3)

• (0, 6)

• (0, -6)

What type of line is used to graph the inequality 3x - 2y ≥ 6?

• Curved line

• Dashed line

• Solid line

• Dotted line

In Example 2, which test point is used to determine the shading direction?

• (2, 2)

• (0, 0)

• (1, 1)

• (3, 3)

In Example 3, what is the slope of the line y = 2x?

• -2

• 2

• 0

• 1

What type of line is used to graph the inequality y ≥ 2x?

• Dotted line

• Solid line

• Dashed line

• Curved line

In Example 3, why can't the origin be used as a test point?

• It is on the line

• It is too far from the line

• It is outside the graph

• It is not a valid point

Which point is used as a test point in Example 3?

• (0, 1)

• (2, 0)

• (1, 0)

• (0, 2)