Graphing Linear Inequalities Concepts

The video tutorial explains how to graph linear inequalities by following a series of steps. First, convert the inequality into an equation to form a boundary line. Then, graph the linear equation using a solid or dashed line based on the inequality type. Next, choose a test point not on the line to determine which region to shade. An example is provided to illustrate graphing y > 3x + 1, demonstrating the process of converting the inequality, graphing the line, selecting a test point, and shading the appropriate region. The tutorial concludes with a recap of the steps.

What is the first step in graphing a linear inequality?

• Change the inequality to an equation

• Choose a test point

• Draw the boundary line

• Shade the region

What does changing the inequality symbol to an equality symbol help you find?

• The shaded region

• The boundary line equation

• The slope

• The test point

How do you graph the linear equation once you have it?

• By using the inequality symbol

• By using the test point

• By using the slope and y-intercept

• By using the x-intercept

What is the purpose of choosing a test point?

• To draw the boundary line

• To decide which region to shade

• To determine the slope

• To find the y-intercept

Which point is commonly used as a test point?

• The x-intercept

• Any point on the line

• The y-intercept

• The origin (0,0)

What do you do if the test point satisfies the inequality?

• Shade the opposite region

• Recalculate the slope

• Change the boundary line type

• Shade the region containing the test point

In the example y > 3x + 1, what type of line is used for the boundary?

• Solid line

• Dotted line

• Thick line

• Dashed line

What is the slope of the line y = 3x + 1?

• 2

• 0

• 1

• 3

What is the y-intercept of the line y = 3x + 1?

• 0

• 2

• 1

• 3

If the test point results in a false inequality, what should you do?

• Shade the region containing the test point

• Recalculate the y-intercept

• Shade the opposite region

• Change the inequality symbol