Understanding Linear Inequalities and Their Graphs

This video tutorial covers the basics of linear inequalities, including their definitions, solutions, and how to graph them. It explains the significance of inequality symbols and how they determine whether a line is dashed or solid. The tutorial provides step-by-step instructions for graphing inequalities and includes two examples to illustrate the process. The first example demonstrates graphing an inequality with a solid line and shading down, while the second example shows graphing with a dashed line and shading up. The video emphasizes the importance of understanding solution regions and how to identify solutions using graphs.

What is the primary characteristic that defines a linear inequality?

• It is always positive.

• It has a constant term.

• It includes an inequality symbol.

• It has a variable.

How can you determine if a point is a solution to a linear inequality?

• By graphing the point.

• By substituting the point into the inequality.

• By checking if the point is on the x-axis.

• By comparing it to the y-intercept.

What does the shaded region in the graph of an inequality represent?

• The y-intercept of the line.

• The solution set of the inequality.

• The slope of the line.

• Points that are not solutions.

What type of line is used when graphing an inequality with a 'greater than' symbol?

• Bold line

• Dotted line

• Dashed line

• Solid line

When graphing the inequality y ≤ 1/2x + 3, what is the slope of the line?

• -3

• 1/2

• 3

• -1/2

In the inequality y ≤ 1/2x + 3, why is the line solid?

• Because it is a horizontal line.

• Because it is a vertical line.

• Because the slope is positive.

• Because the inequality includes 'equal to'.

What happens to the inequality symbol when dividing by a negative number?

• It remains the same.

• It changes direction.

• It becomes a positive symbol.

• It is removed.

In the inequality -2x - 3y < 18, what is the y-intercept after converting to slope-intercept form?

• 6

• -3

• 3

• -6

Why is the line dashed in the graph of y > -2/3x - 3?

• Because the inequality does not include 'equal to'.

• Because the slope is negative.

• Because the y-intercept is negative.

• Because it is a vertical line.

What does shading above the line indicate in the graph of an inequality?

• The line is dashed.

• The line is solid.

• The inequality is greater than.

• The inequality is less than.