Graphing Linear Inequalities Concepts

The video tutorial explains how to graph the inequality y < 3x + 5. It begins by labeling the x and y axes and evaluating y for a specific x value. The tutorial then demonstrates how to graph the line y = 3x + 5 using its slope and y-intercept, emphasizing the use of a dotted line to indicate that the line itself is not included in the solution. Finally, it shows how to shade the area below the line to represent all y-values that satisfy the inequality.

What is the inequality we are asked to graph?

• y ≤ 3x + 5

• y > 3x + 5

• y < 3x + 5

• y = 3x + 5

Tags

CCSS.HSA.REI.D.12

What is the purpose of labeling the axes?

• To confuse the viewer

• To provide a reference for plotting points

• To make the graph colorful

• To add unnecessary details

If x = 1, what is the maximum value y can take?

• 7

• 9

• 8

• 10

Tags

CCSS.8.EE.B.5

What is the slope of the line y = 3x + 5?

• 5

• 2

• 4

• 3

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

What is the y-intercept of the line y = 3x + 5?

• 0

• 5

• 3

• 8

Tags

CCSS.HSA.REI.D.12

Why is the line y = 3x + 5 drawn as a dotted line?

• To indicate it is not part of the solution

• To show it is a solid boundary

• To highlight it is the only solution

• To make it more visible

For x = -1, which y-values are part of the solution?

• y > 3x + 5

• y = 3x + 5

• y < 3x + 5

• y ≥ 3x + 5

Tags

CCSS.HSA.CED.A.3

What does the area under the line represent?

• All y-values greater than 3x + 5

• All y-values equal to 3x + 5

• All y-values less than 3x + 5

• All y-values greater than or equal to 3x + 5

Tags

CCSS.HSA.REI.D.12

How do you determine the region that satisfies the inequality?

• By shading both above and below the line

• By shading below the line

• By shading above the line

• By shading the line itself

Tags

CCSS.HSF-LE.A.1B

What happens to the y-values when x is increased?

• They decrease

• They become zero

• They remain constant

• They increase

Tags

CCSS.HSF-LE.A.1B