Understanding Linear Inequalities

This video tutorial introduces linear inequalities in two variables, explaining how they differ from linear equations. It covers the steps to graph linear inequalities, including determining whether to use dashed or solid lines based on the inequality symbol. The video provides examples of graphing inequalities such as Y > 2X - 3, 3X - 2Y = 12, and X < -2, demonstrating how to test points and shade the appropriate regions. The tutorial emphasizes understanding the graphical representation of solutions and offers tips for accurately plotting lines and regions.

What is the main difference between the solution of a linear equation and a linear inequality?

• A linear equation forms a region, while a linear inequality forms a line.

• A linear equation forms a line, while a linear inequality forms a region.

• Both form lines, but with different slopes.

• Both form regions, but with different boundaries.

When graphing a linear inequality, what type of line is used for '<' or '>' symbols?

• Solid line

• Dotted line

• Double line

• Thick line

What is the purpose of using a test point when graphing a linear inequality?

• To determine which side of the line to shade

• To find the slope of the line

• To calculate the y-intercept

• To verify the equation of the line

In the example Y > 2X - 3, why is the line dashed?

• Because Y is equal to 2X - 3

• Because Y is greater than 2X - 3

• Because Y is less than 2X - 3

• Because Y is not part of the solution

What is the y-intercept of the line Y = 2X - 3?

• -2

• -3

• 3

• 2

In the example 3X - 2Y = 12, what type of line is used?

• Solid line

• Dashed line

• Thick line

• Double line

How do you find the x-intercept of the line 3X - 2Y = 12?

• Set Y = 0 and solve for X

• Set X = 0 and solve for Y

• Set both X and Y to 0

• Use the slope formula

In the example X < -2, what type of line is used?

• Solid line

• Double line

• Thick line

• Dashed line

What does the inequality X < -2 indicate about the line's orientation?

• It is a curved line

• It is a diagonal line

• It is a vertical line

• It is a horizontal line

Why is the test point (0,0) often used when graphing inequalities?

• It is always on the line

• It is easy to calculate

• It is always part of the solution

• It is the midpoint of the graph