Graphing Linear Inequalities in Two

Variables•graph a linear inequality

in two variables

•model a real life situation with a linear inequality.

Recall…Graph n < 3 on a number line.

-3 -2 -1 0 1 2 3 4

Graphing an Inequality in Two Variables

Graph x < 2Step 1: Start by graphing the line x = 2

Now what points would give you less

than 2?

Since it has to be x < 2 we shade everything to

the left of the line.

Graph x -2 on the coordinate plane.

x

y

Graph y > 3 on the coordinate plane.

x

y

Graphing a Linear Inequality

Sketch a graph of y 3

Some Helpful Hints

•If the sign is > or < the line is dashed

•If the sign is or the line will be solid

When dealing with just x and y.

•If the sign > or the shading either goes up or to the right

•If the sign is < or the shading either goes down or to the left

Using What We KnowSketch a graph of x + y < 3

Step 1: Put into slope intercept form

y <-x + 3

Step 2: Graph the line y = -x + 3

When dealing with slanted lines

•If it is > or then you shade above

•If it is < or then you shade below the line

Graph y -3x + 2 on the coordinate plane.

x

y

Instead of testing a point

If in y = mx + b form...

Shade up

Shadedown

Solid line

Dashed line

> <

Graph on the coordinate plane.

3x - 4y > 12-3x -3x-4y > -3x + 12-4 -4

y < x - 33

4

m =

b = -3

3

4

Boundary Linex

y

Graph y -3x + 2 on the coordinate plane.

x

y

Boundary Line

y = -3x + 2

m = -3

b = 2

3

1

Test a point not on the linetest (0,0)

0 -3(0) + 2Not true!

ProblemIf you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have.

Let n = # of nickelsLet d = # of dimes

0.05 n + 0.10 d < 5.00

or

5 n + 10 d < 500

5n + 10d < 500n d

0 50

100 0

0 10 20 30 40 50 60 70 80 90 100n

d

60

50

40

30

20

10

0

Graphing Absolute Value Inequalities

xy 2

Graphing Absolute Value Inequalities

21 xy