Mastering Linear Inequalities and Graphing Techniques

The video tutorial covers solving linear inequalities, starting with an introduction and addressing technical issues. It explains solving inequalities with one and two variables, using number lines and coordinate planes. The tutorial demonstrates graphing inequalities, focusing on half planes, and provides examples using slope-intercept and standard forms, including the cover-up method.

What are the two forms of solving linear inequalities discussed in the introduction?

• One variable and four variables

• Two variables and three variables

• One variable and three variables

• One variable and two variables

When solving a linear inequality with one variable, what does an open circle on the number line represent?

• The number is included in the solution

• The number is not included in the solution

• The number is the only solution

• The number is the maximum value

In a linear inequality with two variables, what does a dotted line on the graph indicate?

• The line represents the x-axis

• The line represents the y-axis

• The points on the line are not included in the solution

• The points on the line are included in the solution

What is the term used to describe the region that contains all solutions to a linear inequality with two variables?

• Full plane

• Double plane

• Quarter plane

• Half plane

When graphing the inequality y < 3x - 2, where should you start on the graph?

• At any random point

• At the y-intercept

• At the x-intercept

• At the origin

What does the slope represent in the inequality y < 3x - 2?

• The rise over run

• The y-intercept

• The x-intercept

• The boundary line

In the inequality y < 3x - 2, which region should be shaded?

• To the left of the line

• On the line

• Below the line

• Above the line

What method can be used to graph a linear inequality in standard form?

• Quadratic method

• Point-slope method

• Cover-up method

• Slope-intercept method

When should a solid line be used in graphing a linear inequality?

• When the inequality is not strict

• When the inequality is strict (e.g., < or >)

• When the inequality includes equality (e.g., ≤ or ≥)

• When the inequality is undefined

If a point on the boundary line satisfies the inequality, what type of line should be used?

• Solid line

• Dashed line

• Dotted line

• No line