review topics inequalities. warm up graph each inequality. 1. x > –5 2. y ≤ 0 3. write –6x...
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Review topics
Inequalities
Warm UpGraph each inequality.1. x > –5 2. y ≤ 0
3. Write –6x + 2y = –4 in slope-intercept form, and graph. y = 3x – 2
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
Notice
open circles
< less than
> greater than
Inequalities and their Graphs
Notice colored in circles
≤ less than or equal to
≥ greater than or equal to
Inequities in coordinate planematch each inequality with a graph.
<
><
>
Objective - To graph linear inequalities in the coordinate plane.
Graph x 3.
Number Line Coordinate Plane
-4 -3 -2 -1 0 1 2 3 4
x 3y
x
x 3
x = 3
Graph y 2.
Number Line Coordinate Plane
-4 -3 -2 -1 0 1 2 3 4
y 2 y
x
y 2
y = -2
2Graph y x 1.3
Boundary Line2y x 13
2m3
b 1
Test a Point2y x 13
20 (0) 13
0 1 False!
y
x
If y = mx + b,solid dashed
shade up
shade down
Graph y x 3.
Boundary Line
y x 3
m 1
b 3
Dashed lineShade up
y
x
11
If y = mx + b,
11
Graph 4x 5y 10.
y
x
4x 5y 10 4x 4x
5y 4x 10 5 5
4y x 25
4m5
b 2
Solid lineShade up
If y = mx + b,
45
Graph 3x 2y 8.
y
x
3x 2y 8 3x 3x
2y 3x 8 2 2
3y x 42
3m2
b 4
Dashed lineShade down
If y = mx + b,
32
Graph 4x 3y 6.
y
x
4x 3y 6 4x 4x
3y 4x 6 3 3
4y x 23
4m3
b 2
Solid lineShade up
If y = mx + b,
43
Graph 3x 2y.
y
x
3x 2y2y 3x2 2
3y x2
3m2
b 0
Dashed lineShade up
If y = mx + b,
32
y
x
4m3
b 2
Dashed lineShade Down
If y = mx + b,
Write the inequality described by the graph below.
4y x 23
-4
+3
Determine whether the given point is a solution to the inequality -2x + 3y < 9.
1) (2, -3) 2x 3y 9 (x, y)
2( ) 3 3( ) 92 4 9 9
13 9 Yes, (2,-3) is a solution.
2) (3, 5) 2x 3y 9 2( ) 33 ( ) 95
6 15 9 9 9
No, (3,5) is not a solution.
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
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.