The document discusses graphing linear inequalities in two variables. It provides examples of graphing single inequalities, determining if ordered pairs are solutions, and graphing systems of inequalities by finding the intersection or union of the regions bounded by the inequalities. The key steps shown are using slope and y-intercept to graph lines representing inequalities and testing points to determine the shaded region.

1. 9.5 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Are the ordered pairs a solution to the problem?
1 1
3
y = x -
( -3,-2)
( -1,3)
1 ( ) 1
3
-2 = -3 -
yes
3 = 1 ( - 1) -
1
no
·
·
-2 = -2
3
3 4
3
¹ -

2. 9.5 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Are the ordered pairs a solution to the problem?
1 1
3
y = x -
( 3,0)
( 4,-3)
0 1 ( ) 1
yes
3 1 ( 4) 1
no
·
·
·
·
= 3 -
3
0 = 0
- = -
3
3 1
3
- ¹

3. 9.5 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Are the ordered pairs a solution to the problem?
1 1
3
y > x -
( -3,-2)
( -1,3)
( 3,0)
yes
yes
( 4,-3)
-2 > -2
3 4
> -
0 > 0
3 1
3
3
- >
·
·
·
no
no
no
no yes .

4. 9.5 - Graphing LinearInequalities
Graphing Inequalities in Two Variables
Graph the solution.
1 1
4
y ³ x -
(1,-4)
( 2,2)
4 3
4
- ³ -
2 1
³ - ·
2
·
no
yes

5. 9.5 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution.
3x + 2y £ 10
( 4,3)
( 0,0)
3 £ -1
0 £ 5
·
3 5
2
y £ - x +
no ·
yes

6. 9.5 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution.
y < 3x
( -2,2)
( 3,3)
2 < -6
3 < 9
·
·
no
yes

7. 9.5 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution.
-3x +5y +15 ³0
( 0,0)
( 2,-3)
·
·
yes
no
3
y ³ 3 x -
5
0 ³-3
-3 ³4 4
5

8. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the Union.
ïî
ïí ì
2
y x
³ -
£ - +
1
2
3
y x

9. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution (Graph the intersection).
ïî
ïí ì
2
y x
³ -
£ - +
1
2
3
y x

10. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the union.
ïî
ïí ì
1
x
y x
< - -
³ -
2
2
2

11. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution. (Graph the intersection)
ïî
ïí ì
1
x
y x
< - -
³ -
2
2
2

12. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution. (Graph the intersection)
î í ì
y x
+ + >
2 3 0
x y
- + <
3 9
ìy > -2x -3
ïî
ïí
3
y < 1 x +
3

13. Graph the following linear system of inequalities.
y ³ 2 x
-
4
y < - 3 x
+
2
x
y
Use the slope and y-intercept
to plot two
points for the first
inequality.
Draw in the line. For ³
use a solid line.
Pick a point and test
it in the inequality.
Shade the appropriate
region.

14. Graph the following linear system of inequalities.
y ³ 2 x
-
4
y < - 3 x
+
2
y ³ x -
³
³
2 4 P o i n t ( 0 , 0 )
0 2 ( 0 ) - 4
0 - 4
The region above the line
should be shaded.
x
y
Now do the same for the
second inequality.

15. Graph the following linear system of inequalities.
y ³ 2 x
-
4
y < - 3 x
+
2
x
y
y < - x +
³ -
3 2
3
P o i n t ( - 2 , - 2 )
- 2 ( - 2 ) + 2
- 2 < 8
The region below the line
should be shaded.

16. Graph the following linear system of inequalities.
y ³ 2 x
-
4
y < - 3 x
+
2
x
y
The solution to this
system of inequalities is
the region where the
solutions to each
inequality overlap. This
is the region above or to
the left of the green line
and below or to the left
of the blue line.
Shade in that region.

17. YYoouu TTrryy OOnnee!!
1. Graph the following linear systems
of inequalities.
y > –x +4
y > x –2

18. y x
y x
4
2
> - +
> -
y Use the slope and y-intercept
x
to plot two
points for the first
inequality.
Draw in the line.
Shade in the
appropriate region.

19. x
y
y x
y x
4
2
> - +
> -
Use the slope and y-intercept
to plot two
points for the second
inequality.
Draw in the line.
Shade in the
appropriate region.

20. x
y
y x
y x
4
2
> - +
> -
The final solution is the
region where the two
shaded areas overlap
(purple region).