Review topics
Inequalities
Warm Up
Graph each inequality.
1. x > –5
3. Write –6x + 2y = –4
in slope-intercept form,
and graph.
y = 3x – 2
2. y ≤ 0
Inequalities and their Graphs
What is a good definition
for Inequality?
An inequality is a statement that
two expressions are not equal
Inequalities
Two types
• Graphing on a number
line:
• Graphing on a
coordinate graph
Inequalities and their Graphs
Terms you see and need to know
to graph inequalities correctly
< less than
> greater than
Notice
open
circles
Inequalities and their Graphs
≤ less than or equal to
≥ greater than or equal to
Notice colored in circles
Inequities in coordinate plane
Objective - To graph linear inequalities in the
coordinate plane.
Graph x  3.
Number Line
x3
-4 -3 -2 -1 0 1 2 3 4
Coordinate Plane
x3
y
x
x=3
Graph y  2.
Number Line
y  2
-4 -3 -2 -1 0 1 2 3 4
Coordinate Plane
y  2
y
x
y = -2
y
2
Graph y  x  1.
3
Boundary Line
2
y  x 1
3
2
b  1
m
3
x
Test a Point
2
y  x 1
3
2
0  (0)  1
3
0  1 False!
If y = mx + b,
solid dashed
shade up
shade down




If y = mx + b,
solid dashed
shade up
shade down




Graph y   x  3.
Boundary Line
y
y  x  3

1
1
m  1 

1 1
b3
If y = mx + b,

Dashed line
Shade up
x
Graph 4x  5y  10.
4x  5y  10
4x
 4x
5y  4x  10
5
5

4
y
x2
5

4
4
m

5
5
b2
If y = mx + b,

Solid line
Shade up
y
x
Graph 3x  2y  8.
3x  2y  8
3x
 3x
2y  3x  8
2
2
3
y x4
2
3

3
m 
2 2
b  4
If y = mx + b,

Dashed line
Shade down
y
x
Graph 4x  3y  6.
4x  3y  6
4x
 4x
3y 
 4x  6
3
3
4
y x2
3
4

4
m 
3 3
b  2
If y = mx + b,

Solid line
Shade up
y
x
Graph 3x  2y.
3x  2y
2y  3x
2 2
3
y x
2
3

3
m 
2 2
b0
If y = mx + b,

Dashed line
Shade up
y
x
Write the inequality described by the graph below.
b2
y
4
m
3
If y = mx + b,
Dashed line
Shade Down
4
y x2
3

-4
+3
x
Determine whether the given point is a solution
to the inequality -2x + 3y < 9.
(x, y)
1) (2, -3)
2x  3y  9
2(2)  3(3)  9
4  9  9
13  9
Yes, (2,-3) is a solution.
2) (3, 5)
2x  3y  9
2(3)  3(5)  9
6  15  9
99
No, (3,5) is
not a solution.
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 + 0.10 d
< 5.00
or
5 n + 10 d < 500
5n + 10d < 500
n
d
d
0
50
60
100
0
50
40
30
20
10
0
n
0 10 20 30 40 50 60 70 80 90 100
Test Yourself
• Click here to go through a multiple choice
question set
ON YOUR OWN:
• Review your
notes. Rewrite
and fortify them if
needed.
• Update your
vocab list, if
needed.
• See worksheet
handed out in class.