Understanding Inequalities and Graphs

The video tutorial explains how to write an inequality that fits a given graph. It starts by identifying the y-intercept and calculating the slope of the line. The equation of the line is then formulated using the slope-intercept form. Finally, the tutorial explains how the inequality includes the line and the area above it, providing a complete understanding of the graph's representation.

What is the first step in writing an inequality that fits a graph?

• Identify the slope of the line

• Determine the y-intercept

• Understand the area the inequality covers

• Find the x-intercept

How can you identify the y-intercept from a graph?

• By looking at the point where the line crosses the y-axis

• By finding where the line crosses the x-axis

• By calculating the slope

• By determining the area above the line

What is the y-intercept of the line in the given graph?

• -1

• 2

• -2

• 0

How is the slope of a line calculated?

• By dividing the change in x by the change in y

• By dividing the change in y by the change in x

• By adding the change in x and y

• By multiplying the change in x by the change in y

What is the slope of the line in the graph?

• 1/2

• -1/2

• 2

• -2

What is the equation of the line in slope-intercept form?

• y = -1/2x - 2

• y = 1/2x + 2

• y = 1/2x - 2

• y = -1/2x + 2

What does the inequality y ≥ -1/2x - 2 represent?

• Only the line

• Only the area above the line

• The line and the area below it

• The line and the area above it

If x = 2, what is the corresponding y-value on the line?

• -3

• 0

• 2

• -1

What does the bold line in the graph indicate?

• The line is below the area of interest

• The line is not part of the inequality

• The line is included in the inequality

• The line is dashed

Why is the area above the line shaded in the graph?

• Because y is less than the line

• Because y is equal to the line

• Because y is greater than or equal to the line

• Because y is not related to the line