Graphing Inequalities and Test Points

The video tutorial explains how to graph the inequality x > 3. It begins by discussing various methods for graphing, such as finding intercepts and using slope-intercept form, but focuses on a simpler approach. The tutorial demonstrates how to graph the boundary line x = 3, which is a vertical line, and explains that since x > 3, the line should be dashed. Test points are used to determine which side of the line represents the solution set, and the area to the right of the line is shaded to indicate the solution region.

What is the first step in graphing the inequality x > 3?

• Create a table of values

• Graph the line x = 3

• Use slope-intercept form

• Find the y-intercept

What type of line is used to represent x = 3 on the graph?

• Horizontal line

• Vertical line

• Curved line

• Diagonal line

Why is the line x = 3 not part of the solution for x > 3?

• Because x = 3 is equal to 3

• Because x = 3 is not greater than 3

• Because x = 3 is a horizontal line

• Because x = 3 is less than 3

What type of line is used to indicate that x = 3 is not part of the solution?

• Bold line

• Solid line

• Dotted line

• Dashed line

Which test point can be used to determine the solution side of the line x = 3?

• (4, 0)

• (0, 0)

• (3, 0)

• (5, 0)

What is the result of testing the point (0, 0) for the inequality x > 3?

• False

• Cannot be determined

• Undefined

• True

What is the result of testing the point (4, 0) for the inequality x > 3?

• Cannot be determined

• Undefined

• False

• True

What does shading the area to the right of the line x = 3 represent?

• The solution set for x < 3

• The solution set for x > 3

• The boundary line

• The x-intercept

Why is a dashed line used instead of a solid line for the boundary?

• To indicate the line is part of the solution

• To indicate a vertical line

• To represent a horizontal line

• To show the line is not part of the solution

What does the inequality x > 3 mean in terms of graphing?

• All points to the right of x = 3 are included

• Only the point x = 3 is included

• All points to the left of x = 3 are included

• All points on the line x = 3 are included