Graphing Linear Inequalities: Key Concepts and Techniques

This video tutorial explains how to graph linear inequalities on a coordinate plane. It begins with a quick review of graphing linear equations using slope and y-intercept. The tutorial then covers graphing inequalities with different symbols: greater than or equal to, greater than, less than or equal to, and less than. For each type, it explains how to determine whether the line should be solid or dashed and how to shade the appropriate region. The video also emphasizes the golden rule of inequalities, which requires flipping the inequality sign when dividing by a negative number. The tutorial concludes with a recap and a preview of a follow-up video on solving systems of inequalities.

What is the slope of the line described in the video?

• -2

• 2

• -1

• 1

What is the y-intercept of the line discussed in the video?

• -2

• 4

• 2

• -4

What does a solid line represent in the context of inequalities?

• Only negative values

• Inclusive of the line values

• Exclusive of the line values

• Only positive values

What does the shading above the line represent in the context of inequalities?

• y is greater than the expression

• x is greater than the expression

• y is less than the expression

• x is less than the expression

Is the point (9, 2) a solution to the inequality y ≥ -2x + 4?

• Only if y is negative

• Only if x is negative

• No

• Yes

What change occurs to the line when the inequality symbol is just 'greater than'?

• Becomes dashed

• Becomes thicker

• No change

• Becomes thinner

Is the point (-1, 6) still a solution when the line is dashed?

• Yes

• Only in positive quadrants

• No

• Only in negative quadrants

If a line is dashed in an inequality graph, are points on the line included in the solution set?

• Yes

• No

• Only if y > 0

• Only if x > 0

What does shading below the line indicate?

• y is greater than the expression

• x is less than the expression

• x is greater than the expression

• y is less than the expression

When dividing by a negative number, what must you do to the inequality symbol?

• Flip it

• Remove it

• Double it

• Halve it