Understanding and Graphing Inequalities

The video tutorial explains how to graph the inequality y - 4x < -3. It begins by transforming the inequality into slope-intercept form, y < 4x - 3. The tutorial then demonstrates how to graph the boundary line y = 4x - 3 using a dotted line to indicate that it is not part of the solution. The solution region is identified as the area below this line. The video also includes testing points to verify which side of the boundary line satisfies the inequality.

What is the first step in converting the inequality y - 4x < -3 into slope-intercept form?

• Multiply both sides by 4

• Add 4x to both sides

• Divide both sides by 4

• Subtract 4x from both sides

What does the slope-intercept form of the inequality y - 4x < -3 look like?

• y > 4x - 3

• y > 4x + 3

• y < 4x + 3

• y < 4x - 3

Why is it important to understand the boundary line when graphing the inequality?

• It indicates the y-intercept

• It helps determine the slope

• It defines the solution region

• It shows the x-intercept

How is the boundary line of the inequality y < 4x - 3 represented on the graph?

• As a dashed line

• As a solid line

• As a dotted line

• As a bold line

What is the significance of the dotted line in the graph of the inequality?

• It is part of the solution

• It represents the y-axis

• It is not part of the solution

• It represents the x-axis

Which point would you test to determine if it lies in the solution region of the inequality?

• (0, 0)

• (1, 1)

• (2, 0)

• (3, 0)

What does it mean if a point satisfies the inequality y < 4x - 3?

• The point is above the boundary line

• The point is on the x-axis

• The point is below the boundary line

• The point is on the boundary line

How can you verify that a point is part of the solution region?

• Check if it is above the boundary line

• Check if it satisfies the inequality

• Check if it lies on the boundary line

• Check if it is on the y-axis

What is the final step in graphing the inequality y < 4x - 3?

• Draw a solid line

• Shade the region above the line

• Draw a bold line

• Shade the region below the line

Why is it important to test points when graphing inequalities?

• To determine the slope

• To find the x-intercept

• To verify the solution region

• To find the y-intercept