Understanding Linear Inequalities

The video tutorial explains how to write linear inequalities from graphs by first determining the linear equation of the boundary line in slope-intercept form. It covers two examples: one with a dashed boundary line and another with a solid boundary line. The tutorial demonstrates how to identify the slope and y-intercept, determine the inequality symbol based on the boundary line type, and verify the inequality by selecting a point in the shaded region.

What is the first step in writing a linear inequality for a graph?

• Identify the shaded region

• Select a test point

• Determine if the line is dashed or solid

• Find the linear equation of the boundary line

In the first example, what is the y-intercept of the boundary line?

• (0, 2)

• (0, 0)

• (0, 1)

• (0, 3)

How is the slope determined in the first example?

• By dividing the vertical change by the horizontal change

• By subtracting the y-coordinates of two points

• By adding the x-coordinates of two points

• By dividing the horizontal change by the vertical change

What inequality symbol is used for a dashed boundary line?

• Greater than or equal to

• Less than or greater than or equal to

• Less than or greater than

• Less than or equal to

Which point is used to verify the inequality in the first example?

• (1, 0)

• (0, 1)

• (2, 3)

• (3, 2)

In the second example, what is the y-intercept of the boundary line?

• (0, 1)

• (0, 0)

• (0, 3)

• (0, 2)

What is the slope of the boundary line in the second example?

• 2

• -1

• 0

• 1

What inequality symbol is used for a solid boundary line?

• Less than or equal to

• Greater than

• Greater than or equal to

• Less than

Which point is used to verify the inequality in the second example?

• (3, 2)

• (0, 5)

• (2, 3)

• (5, 0)

What is the final inequality for the second example?

• y ≤ x + 3

• y > x + 3

• y < x + 3

• y ≥ x + 3