Graphing Linear Inequalities: Key Concepts and Techniques

This video tutorial provides an in-depth lesson on graphing linear inequalities. It begins with a review of solving simple equations and inequalities, then moves on to graphing these inequalities on a coordinate plane. The tutorial explains how to use solid and dashed lines to represent different types of inequalities and demonstrates shading techniques to identify solution sets. Through examples, viewers learn to determine whether points are solutions based on their position relative to the line and shaded regions. The lesson concludes with a recap of the key concepts covered.

What is the solution to the equation X + 5 = 8?

• X = 2

• X = 4

• X = 3

• X = 5

If X + 5 > 8, which of the following is true?

• X ≥ 3

• X > 3

• X ≤ 3

• X < 3

How do you represent the solution to X > 3 on a number line?

• Closed circle at 3, shade to the right

• Open circle at 3, shade to the right

• Closed circle at 3, shade to the left

• Open circle at 3, shade to the left

In graphing the inequality Y ≥ X, where do you shade?

• Below the line

• Above the line

• On the line

• No shading required

What type of line is used for the inequality Y > X?

• Solid line

• No line

• Dashed line

• Dotted line

For the inequality Y ≥ 3X - 2, where do you start graphing?

• At the origin

• At the y-intercept -2

• At the point (3, -2)

• At the x-intercept 3

What does the shading above the line represent in the inequality Y ≥ 3X - 2?

• Points below the line

• Points that are solutions

• Points that are not solutions

• Points on the line

Which point is a solution to the inequality Y ≥ 3X - 2?

• (2, 4)

• (-5, 5)

• (6, 0)

• (0, 0)

For the inequality Y < -1/2X + 4, what type of line is used?

• Dotted line

• No line

• Dashed line

• Solid line

Which point is not a solution to the inequality Y < -1/2X + 4?

• (6, 8)

• (2, 1)

• (0, 4)

• (0, 0)