Graphing Linear Inequalities

The video tutorial explains how to graph the inequality y < 3x + 5. It begins by discussing the concept of graphing inequalities and the importance of using a dotted line to represent that the line itself is not included in the solution. The tutorial then details how to plot the line y = 3x + 5, including identifying the y-intercept and slope. It further explains why a dotted line is used and provides examples to illustrate how to determine which y-values are less than 3x + 5 for given x-values. The tutorial concludes by emphasizing that the solution includes all points below the dotted line.

What is the inequality that needs to be graphed?

• y > 3x + 5

• y ≤ 3x + 5

• y < 3x + 5

• y = 3x + 5

What is the y-intercept of the line y = 3x + 5?

• 3

• 0

• 5

• 8

What does the slope of 3 indicate in the line y = 3x + 5?

• Move 1 unit down for every 3 units left

• Move 3 units down for every 1 unit left

• Move 1 unit up for every 3 units right

• Move 3 units up for every 1 unit right

Why is a dotted line used for the inequality y < 3x + 5?

• To include the line in the solution

• To exclude the line from the solution

• To indicate a solid boundary

• To show a vertical line

If x = 0, what is the value of y in the inequality y < 3x + 5?

• y < 0

• y < 8

• y < 5

• y < 3

If x = 1, what is the value of y in the inequality y < 3x + 5?

• y < 10

• y < 8

• y < 5

• y < 3

What does the area below the dotted line represent in the graph of y < 3x + 5?

• Values of y greater than 3x + 5

• Values of y greater than or equal to 3x + 5

• Values of y equal to 3x + 5

• Values of y less than 3x + 5

What would change if the inequality was y ≤ 3x + 5?

• The y-intercept would change

• The slope would change

• The line would be solid

• The line would be dotted

What is the significance of the dotted line in the graph of y < 3x + 5?

• It shows a horizontal line

• It shows a vertical line

• It indicates the line is excluded

• It indicates the line is included

What does the inequality y < 3x + 5 tell you about the values of y?

• y is greater than 3x + 5

• y is equal to 3x + 5

• y is less than 3x + 5

• y is greater than or equal to 3x + 5