Linear Inequalities and Their Graphs

The video tutorial explains how to graph a linear inequality, specifically y > 3x - 2. It covers the general form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. The tutorial demonstrates how to plot the graph by identifying the y-intercept and using the slope to find additional points. It also explains the difference between solid and dashed lines based on the inequality symbol. Finally, it shows how to test points to determine which side of the line to shade, using the origin as a test point when applicable.

What is the general form of a linear equation?

• y = a/x + b

• y = mx^2 + b

• y = mx + b

• y = ax^2 + bx + c

In the equation y = mx + b, what does 'b' represent?

• The slope

• The origin

• The x-intercept

• The y-intercept

How do you determine the slope from the equation y = 3x - 2?

• The slope is -2

• The slope is 2

• The slope is 3

• The slope is 1/3

What type of line is used for the inequality y > 3x - 2?

• Dotted line

• Dashed line

• Bold line

• Solid line

If the inequality is y ≥ 3x - 2, what type of line should be drawn?

• Solid line

• Dotted line

• Bold line

• Dashed line

What is the best test point to use when determining the shading area?

• (1,1)

• (0,0)

• (2,2)

• (-1,-1)

Why is (0,0) often used as a test point?

• It simplifies calculations

• It is always below the line

• It is always above the line

• It is always on the line

What should you do if the test point (0,0) lies on the line?

• Do not shade at all

• Shade below the line

• Shade above the line

• Use another test point

If a point satisfies the inequality, where should you shade?

• On the line

• Away from the point

• Do not shade

• Towards the point

What happens if a point does not satisfy the inequality?

• Do not shade at all

• Shade towards the point

• Shade away from the point

• Shade on the line