Graphing Linear Inequalities Explained

The video tutorial explains how to graph linear inequalities by using shading and different line types. It covers the process of identifying the slope and y-intercept, and how the inequality symbol determines whether to use a solid or dashed line and where to shade on the graph. Several examples are provided to illustrate these concepts, including graphing inequalities like y ≤ 3/2x + 2, y < 3/2x + 2, and y ≥ 3/2x + 2. The tutorial concludes with practice problems to reinforce the learning.

What type of line is used when the inequality symbol includes 'less than or equal to'?

• Dashed line

• Solid line

• No line

• Dotted line

When graphing 'y < 3/2x + 2', where should the shading be applied?

• On the line

• Below the line

• Above the line

• No shading needed

What does a dashed line indicate in a graph of an inequality?

• The line is an axis

• Inclusion of the line in the solution set

• Exclusion of the line from the solution set

• The line is undefined

For the inequality 'y > 2x - 3', how is the line graphed?

• Dotted line

• Solid line

• Dashed line

• No line

In the context of graphing inequalities, what does shading above the line signify?

• y is less than the expression

• y is equal to the expression

• y is greater than the expression

• No relationship

How do you transform the inequality '-3y ≤ x - 15' to 'y = mx + b' form?

• Multiply both sides by -3

• Subtract x from both sides

• Divide both sides by -3 and reverse the inequality

• Add 15 to both sides

What is the correct graphing approach when the inequality symbol is 'greater than'?

• Dashed line with no shading

• Solid line with shading above

• Dashed line with shading above

• Solid line with shading below

What is the slope of the line represented by the equation 'y = -1/3x + 5'?

• -3

• 1/3

• -1/3

• 5

What does the y-intercept of 'y = -1/3x + 5' indicate on the graph?

• The maximum value of y

• The x-coordinate where the line crosses the y-axis

• The slope of the line

• The y-coordinate where the line crosses the y-axis

Before submitting the graphed inequalities, what final check is necessary?

• Ensure all lines are dashed

• Confirm the shading is correct

• Verify the graph is in color

• Label the lines with their equations