Lesson 6-6
Objective - To graph linear inequalities in the
coordinate plane.
Graph y > −2.
Graph x ≤ 3.
Number Line
Coordinate Plane
x≤3
Number Line
y > −2
x≤3
y
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4
Coordinate Plane
y > −2
y
x
x
y = -2
x=3
y
Graph y ≤ 2 x − 1.
3
Graph y > − x + 3.
Boundary Line
Boundary Line
y = 2 x −1
3
2
b = −1
m=
3
y = −x + 3
m = − 1 = −1 = 1
1 −1
b=3
x
Test a Point
y ≤ 2 x −1
3
0 ≤ 2 (0) − 1
3
0 ≤ −1 False!
Graph 4x + 5y ≥ 10.
4x + 5y ≥ 10
−4x
− 4x
5y ≥ −4x + 10
5
5
y ≥ −4 x + 2
5
−
4
m=
= 4
5
−5
b=2
If y = mx + b,
≥
Solid line
Shade up
y
If y = mx + b,
If y = mx + b,
>
solid dashed
shade up
shade down
≥
≤
x
>
<
y
x
Dashed line
Shade up
Graph 3x − 2y > 8.
3x − 2y > 8
−3x
− 3x
−2y <> −3x + 8
−2
−2
y< 3x−4
2
3
m = = −3
2 −2
b = −4
y
If y = mx + b,
<
Dashed line
Shade down
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010
x
Lesson 6-6 (cont.)
Graph 4x − 3y ≤ 6.
4x − 3y ≤ 6
−4x
− 4x
−3y ≥
≤ −4x + 6
−3
−3
4
y≥ x−2
3
4
m = = −4
3 −3
b = −2
y
x
Graph 3x < 2y.
3x < 2y
2y > 3x
2
2
y> 3x
2
m = 3 = −3
2 −2
b=0
If y = mx + b,
≥
x
If y = mx + b,
>
Solid line
Shade up
Write the inequality described by the graph below.
b=2
Dashed line
Shade up
Determine whether the given point is a solution
to the inequality -2x + 3y < 9.
(x, y)
y
m=−4
3
−2x + 3y < 9
−2(2) + 3(−3) < 9
−4 + −9 < 9
−13 < 9
1) (2, -3)
-4
If y = mx + b,
+3
<
Dashed line
Shade Down
y
Yes, (2,-3) is a solution.
x
2) (3, 5)
y<−4x+2
3
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
−2x + 3y < 9
−2(3) + 3(5) < 9
−6 + 15 < 9
9<9
No, (3,5) is
not a solution.
5n + 10d < 500
n
d
d
0
50
60
100
0
50
40
30
<
5.00
or
5 n + 10 d < 500
20
10
0
n
0 10 20 30 40 50 60 70 80 90 100
Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010