Warm-Up

Solve the following Inequalities:

1.

2.

3.

7 154

8 6 7

14 2 4

x

x

x

Warm-Up Answers

1.

2.

3.

32

2 or 2

5 or 5

x

x x

x x

Lesson 6.2 Graphing Inequalities

In Slope-Intercept Form

It could be greater than (>) or less than (<)

or (>) or (<).

Graphing linear inequalities with 2 variables

The graph of the solutions to a single inequality is called a ____________

because it includes all the points in the coordinate plane that fall on one side of

the __________ line.

half-plane

boundary

boundary

To Graph an Inequality:

You must follow these 5 steps: 1. Put in y = mx + b form.2. Find m and b.3. Decide if the line is solid or dotted.

<, > dotted line <, > solid line

4. Graph using your m and b5. Shade above or below the line using: Test Point Method! (0, 0) is the easiest! But we cannot

always test this point so we have to find another point that is clearly above or below the line.If the point you plug in makes a TRUE statement, shade where that point is included. If the point you plug in makes a FALSE statement, shade away from that point.

Example 1:

1. Find m and b. m =-2/3

b = (0, 2)

Dotted line

22

3y x

2. Is the line dotted or solid?

3. Next, let’s graph so can pick a test point to try!

20 (0) 2

3

22

3y x

0 2

Use (0, 0) as a test point, and plug into

the formula

22

3y x

Is this a true statement?

NO! Which means we shade AWAY from that point…

Example 2:1. m = ¼

2. b = (0, 3)

3. Solid Line

4. Test Point

(0, 0)

13

4y x

13

4y x

10 (0) 3

4

0 3Which is true so shade where that point exists!

Example 3: y < – 3x + 1Try this one on your own!

m =

b = (0, )

Dotted or Solid Line?

Test Point?

Lesson 6.3

Solving and Graphing Inequalities in Standard Form

You have two options for graphing in standard form.

• Solve for y by getting into slope intercept form.

• Plug in your zeros to get x and y intercepts (assuming equal sign).

• Then use a test point on either side for shading.

Ex. 4 2x + y < 4

2 4x y

Easily Solve for y

-2x -2x 2 4y x

Graph the y intercept (0,4)

Now, graph two more points using the slope (m=-2)

Draw a dotted line through the points (It is dotted because there is not an = sign under the inequality)

Pick a test point to see which side of the line to shade. Let’s use (4, 5)

Plug the ordered pair into the original equation 5<-2(4) + 4. Is this true? Only shade the true side. Since this false we will shade the other side of the line

Ex. 5 2 4 8x y -2x -2x

824 xy-4 -4

22

1 xy

2,02

1

b

m

Pick a test point to see which side of the line to shade. Let’s use (0, 0)

Plug the ordered pair into the original equation. Is this true? Only shade the

true side.

You try!

32

3 xy

3,02

3

b

m

12

1 xy

1,02

1

b

m

Ex. 6 Ex. 7

Summary/Reflection

How will you remember when to use a solid or dotted line?

and

How will you remember where to shade on a linear inequality?

ClassworkWorksheet 6.2-6.3

HomeworkWorksheet 6.2-6.3