Lesson: Graphing Linear Inequalities

Multiple Choice

Do you have your phone in the box, notebook out, and ready to take notes? ​

(you will need to take a picture and upload it at the end)

• YES I have my notebook out

• No, I know it means a bad grade

Graphing Linear Inequalities

Objective: Graph linear inequalities and determine solutions.

Graphing

Graph: y = 4x - 3

​Graphing Equations and Inequalities

​Graphs of inequalities are similar to linear equations because they both have points on a coordinate plane and a line connecting the points. However, a linear equation is ONLY the line but an inequality extends beyond that line.

​y < 2x - 1

​Graphing Linear Inequalities

​The inequality symbol tells you if the line in the graph is a SOLID or a DOTTED line.

< or > DOTTED line 

≤ or ≥ SOLID line 

​y ≤ 2x - 1

​y < -3x + 1

​Graphing Linear Inequalities

​The inequality symbol tells you to SHADE ABOVE or SHADE BELOW the line.

< or ≤ Shade BELOW 

> or ≥ Shade ABOVE 

​y ≥ -3x + 1

Match

Match the following symbol with how you would graph the inequality.

• <

• >

• ≤

• ≥

Dotted Line Shaded Below

Dotted Line Shaded Above

Solid Line Shaded Below

Solid Line Shaded Above

• Dotted Line Shaded Below

• Dotted Line Shaded Above

• Solid Line Shaded Below

• Solid Line Shaded Above

Match

Match the following graphs with the inequality.

y < 2x + 1

y ≤ 2x + 1

y > 2x + 1

y ≥ 2x + 1

• y < 2x + 1

• y ≤ 2x + 1

• y > 2x + 1

• y ≥ 2x + 1

​Graphing Vertical Linear Inequalities

​x = -2

​x < -2

​x ≥ -2

​Graphing Horizontal Linear Inequalities

​y = -2

​y < -2

​y ≥ -2

Match

Match the following inequality with its graph.

x < 3

x > 3

y < 3

y > 3

• x < 3

• x > 3

• y < 3

• y > 3

​Solutions to Linear Inequalities

​Points that lie in the shaded region and if the line is solid, points that lie on the line.

​y < -3x + 1

​y ≥ -3x + 1

Multiple Choice

Which point is a solution to y > 4x - 3?

• (-1, 3)

• (-2, 1)

• (-1, -10)