Graphing Two-Variable Linear Inequalities

The video tutorial explains how to graph inequalities on a coordinate plane. It begins with graphing the line y = 4x + 3, identifying the y-intercept and slope. The tutorial then explores the concept of inequalities, specifically what it means for y to be less than or equal to 4x + 3, and how to represent this on a graph by shading the area below the line. The video also covers graphing y > -x/2 - 6, demonstrating the use of dashed lines to indicate that the line itself is not included in the solution set. The tutorial provides a clear understanding of graphing linear inequalities and the conventions used in their representation.

What does the inequality y ≤ 4x + 3 mean?

• y is greater than 4x + 3

• y is less than or equal to 4x + 3

• y is less than 4x + 3 but not equal

• y is only equal to 4x + 3

Tags

CCSS.HSA.REI.D.12

How do you find the y-intercept of the line y = 4x + 3?

• By setting x to 0

• By setting y to 0

• By adding 3 to the slope

• By multiplying the slope by x

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

What does a slope of 4 indicate in the line y = 4x + 3?

• For every 4 units up, move 1 unit right

• For every 1 unit up, move 4 units right

• For every 1 unit right, move 4 units up

• For every 4 units right, move 1 unit up

Tags

CCSS.8.EE.B.5

How do you represent the inequality y < 4x + 3 on a graph?

• By shading above the line

• By shading below the line

• By drawing a dashed line

• By drawing a solid line

Tags

CCSS.HSA.REI.D.12

When graphing y < 4x + 3, why do we shade below the line?

• To indicate the line is not part of the solution

• To represent all y values less than 4x + 3

• To represent all y values greater than 4x + 3

• To represent all y values equal to 4x + 3

Tags

CCSS.HSA.REI.D.12

What is the y-intercept of the line y = -1/2x - 6?

• 1/2

• 6

• -1/2

• -6

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

What does the slope of -1/2 indicate for the line y = -1/2x - 6?

• For every 1 unit right, move 2 units up

• For every 1 unit right, move 2 units down

• For every 2 units right, move 1 unit down

• For every 2 units right, move 1 unit up

Tags

CCSS.8.EE.B.5

How is the inequality y > -x/2 - 6 graphically represented?

• By using a solid line

• By shading the area above the line

• By using a dashed line

• By shading the area below the line

Tags

CCSS.HSA.REI.D.12

In the context of inequalities, what does shading above a line represent?

• All y values not included in the solution

• All y values less than the line equation

• All y values greater than the line equation

• All y values equal to the line equation

Tags

CCSS.HSA.REI.D.12

What does it mean if a line is dashed in the context of graphing inequalities?

• The line itself is not included in the solution

• Only the area above the line is included

• The line itself is included in the solution

• Only the area below the line is included

Tags

CCSS.HSA.REI.D.12