Graphing Inequalities and Line Types

The video tutorial explains how to graph inequalities and systems of inequalities. It covers the decision-making process for using solid or dotted lines based on inequality symbols. The tutorial provides examples of graphing y < x + 3 with a dotted line and y ≥ 2x - 2 with a solid line. It emphasizes the importance of using a ruler for accuracy and mentions that shading, a crucial step in graphing inequalities, will be covered in another video. The tutorial concludes with a reminder of the rules for choosing line types and hints at future examples involving horizontal and vertical lines.

What is the first step when graphing an inequality?

• Choose a color for the line

• Calculate the y-intercept

• Decide whether to use a solid or dotted line

• Determine the slope of the line

Which symbol indicates that a dotted line should be used?

• ≥

• <

• >

• ≤

For the inequality y < x + 3, which of the following points is on the line?

• (1, 4)

• (2, 5)

• (-3, 0)

• (0, 3)

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

• Because it is a vertical line

• Because it does not include points on the line

• Because it is a horizontal line

• Because it includes points on the line

What is the inequality for the second example in the video?

• y < x + 3

• y ≥ 2x - 2

• y > 2x - 2

• y ≤ 2x - 2

Which points are used to graph the inequality y ≥ 2x - 2?

• (0, -2), (2, 2), (1, 0)

• (1, 4), (-3, 0), (0, 3)

• (2, 5), (3, 1), (4, 0)

• (0, 0), (1, 1), (2, 2)

Why is a solid line used for the inequality y ≥ 2x - 2?

• Because it does not include points on the line

• Because it is a vertical line

• Because it includes points on the line

• Because it is a horizontal line

What is the final step in graphing inequalities, as mentioned in the video?

• Shading the region

• Labeling the axes

• Drawing the line

• Calculating the slope

What does the symbol '≥' indicate when graphing an inequality?

• Graph a horizontal line

• Graph a vertical line

• Use a solid line

• Use a dotted line

Which of the following inequalities would use a solid line?

• y < x + 3

• y > x - 1

• y < 2x + 5

• y ≤ x + 2