1. Graphing Linear Inequalities in Two Variables
graph a linear inequality in two variables
model a real life situation with a linear inequality.

2. Recall…
Graph n < 3 on a number line.

3. Graphing an Inequality in Two Variables
Graph x < 2
Step 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.

4. Graph x -2 on the coordinate plane.y x

5. Graph y > 3 on the coordinate plane.x

6. Graphing a Linear Inequality
Sketch a graph of y  3

7. 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

8. Step 1: Put into slope intercept form
Using What We Know
Sketch a graph of x + y < 3
Step 1: Put into slope intercept form
y <-x + 3
Step 2: Graph the line y = -x + 3

9. When dealing with slanted lines
If it is > or  then you shade above
If it is < or  then you shade below the line

10. > < Graph y -3x + 2 on the coordinate plane. y
Instead of testing a point
If in y = mx + b form...
Shade up
Shade
down
Solid
line x
>
<
Dashed
line

11. -3x -3x -4y > -3x + 12 -4 -4 Graph on the coordinate plane.
y < x - 3 x
Boundary Line
m =
b = -3

12. Graph y -3x + 2 on the coordinate plane.
Boundary Line
y = -3x + 2
m = -3
b = 2 x
Test a point not on the line
test (0,0)
(0) + 2
Not true!

13. Problem
If 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 nickels
Let d = # of dimes
0.05 n d < 5.00 or
5 n + 10 d < 500

14. 5n + 10d < 500 n d d 50 60 50 40 30 20 10
100 n

15. Graphing Absolute Value Inequalities

16. Graphing Absolute Value Inequalities