Graphing Inequalities

6.7 Graphing Linear Inequalities

Don't Forget to Shade

Let's Review Slope-Intercept Form

• slope "m"

• y-intercept "b"

Review how to graph:

Begin with your intercept

Move with your slope

Multiple Choice

What is the slope in the following equation?

y = -2x + 6

• 6

• -2

• -2x

Multiple Choice

What is the slope in the following equation?

y = -8 - 3x

• -3x

• -3

• -8

Multiple Choice

What is the y-intercept in the following inequality?

y > -8 - 3x

• -8

• -3

Multiple Choice

What is the y-intercept in the following inequality?

y < 1/2x + 3

• 1

• 2

• 3

• 1/2

Let's Review Graphing Inequalities

•  $\le\&\ge\ solid\ circle\ \left(closed\right)$  

•  $<\&>\ open\ circle$  

Multiple Choice

Which inequality is graphed?

• $$x>5$$
  

• $$x<5$$
  

• $$x\le5$$

• $$x\ge5$$

Multiple Choice

Which inequality is graphed?

• $$x>-1$$
  

• $$x<-1$$
  

• $$x\le-1$$

• $$x\ge-1$$

Multiple Choice

Which inequality is graphed?

• $$x>3$$
  

• $$x<3$$
  

• $$x\le3$$

• $$x\ge3$$

Multiple Choice

Which inequality is graphed?

• $$x>5$$
  

• $$x<5$$
  

• $$x\le5$$

• $$x\ge5$$

Let's Merge Graphing Lines & Inequalities

"Graphing Linear Inequalities"

Two new things to add to our graphs:

• Solid/dashed boundary lines

• Shading above or below the boundary line

How do you know when it's a solid or dashed boundary line?

•  $\le\&\ge\ will\ be\ solid$  

•  $<\&>\ will\ be\ dashed$  

Multiple Choice

Will this inequality have a solid or dashed boundary line?

$$y\ \ge\ 2x\ -\ 3$$  

• solid

• dashed

Multiple Choice

Will this inequality have a solid or dashed boundary line?

$$y\ \le\ \frac{2}{3}x\ +\ 8$$  

• solid

• dashed

Open Ended

Will this inequality have a solid or dashed boundary line?

$$y\ <-3x\ -\ 9$$  

Open Ended

Will this inequality have a solid or dashed boundary line?

$$y\ >-3x\ -\ 9$$  

Open Ended

Will this inequality have a solid or dashed boundary line?

$$y\ \ge\frac{1}{4}x\ +\ 2$$  

Open Ended

Will this inequality have a solid or dashed boundary line?

$$y\ >\frac{1}{4}x\ +\ 2$$  

Open Ended

Will this inequality have a solid or dashed boundary line?

$$y\ \ge x$$  

How do you shade?

• 
  
   $\le\&<\ is\ below\ the\ line$  
  

•  $\ge\&>\ is\ above\ the\ line$  

Open Ended

Does the following graph show the shaded region below or above the boundary line?

Open Ended

Does the following graph show the shaded region below or above the boundary line?

Open Ended

Does the following graph show the shaded region less than or greater than the boundary line?

Open Ended

Does the following graph show the shaded region less than or greater than the boundary line?

Open Ended

Does the following graph show the shaded region less than or greater than the boundary line?

Multiple Choice

Which of the following has the shaded region less than the boundary line?

Multiple Choice

Which of the following has the shaded region less than the boundary line?

Multiple Choice

Identify the graph that has the shaded region above the boundary line?

Describe the inequality's boundary line and shaded region.

• solid line

• shade below

Describe the inequality's boundary line and shaded region.

• solid line

• shade above

Describe the inequality's boundary line and shaded region.

• dashed line

• shade below

Describe the inequality's boundary line and shaded region.

• dashed line

• shade above

Open Ended

Describe the inequality's boundary line and shaded region.

$$y\ <\ \frac{1}{2}x\ +\ 2$$  

Open Ended

Describe the inequality's boundary line and shaded region.

$$y\ \ge\ \frac{1}{2}x\ +\ 2$$  

Open Ended

Describe the inequality's boundary line and shaded region.

$$y\ \ge\ -x\ -\ 3$$  

Open Ended

Describe the inequality's boundary line and shaded region.

$$y\ >\ 4x$$  

Open Ended

Describe the inequality's boundary line and shaded region.

$$y\ \ge x\ +\ 9$$  

Open Ended

Describe the inequality's boundary line and shaded region.

$$y\ \le\ x\ +\ 7$$  

Open Ended

Describe the inequality's boundary line and shaded region.

$$y\ <\ -2x\ +\ 1$$