Exploring Rational Expressions: Addition and Subtraction

The video tutorial covers systems of linear inequalities, focusing on graphing them on a coordinate plane. It explains how to determine the solution area by checking points and shading the correct regions. The tutorial includes examples of graphing inequalities in both slope-intercept and standard forms, emphasizing the importance of solid and broken lines. The lesson concludes with verifying solutions by testing points within the shaded regions.

What is the main goal when graphing a system of linear inequalities?

• To find the slope of each line.

• To find the x-intercept of each line.

• To find the intersection of the solution areas.

• To determine the y-intercept of each line.

When graphing the inequality y < x + 3, what type of line should be used?

• Thick line

• Dotted line

• Solid line

• Dashed line

Which test point is commonly used to determine the shading region for an inequality?

• (1,1)

• (0,0)

• (3,3)

• (2,2)

What is the slope of the line for the inequality y > 2x?

• -2

• 2

• 1

• 0

How do you determine which side of the line to shade for the inequality y > 2x?

• Shade above the line by default.

• Use the x-intercept to determine the shading.

• Shade below the line by default.

• Use a test point and check if it satisfies the inequality.

What is the purpose of finding the overlap of the shaded regions?

• To determine the slope of the lines.

• To find the solution to the system of inequalities.

• To check the x-intercept.

• To identify the y-intercept.

Which point was used to verify the solution in the overlap region?

• (2,2)

• (0,0)

• (1,1)

• (4,-1)

When graphing inequalities in standard form, what is the first step?

• Determine the type of line.

• Find the y-intercept.

• Find the slope.

• Create a mini table of values.

What type of line is used for the inequality 4x + 3y > 12?

• Solid line

• Dashed line

• Dotted line

• Thick line

If the test point (0,0) does not satisfy the inequality, where should you shade?

• Below the line

• Above the line

• On the opposite side of the test point

• On the test point