Download Section 4.6

4.6
Graphing Linear Inequalities
1. Determine whether an ordered pair is a solution for a
linear inequality with two variables.
2. Graph linear inequalities.
3x - 2y ≤ 6
2
34
y  x
5
5
Objective 1
Determine whether an ordered pair
is a solution for a linear inequality
with two variables.
Checking an Ordered Pair
1. Replace the variables with the corresponding
values
2. Is the inequality true?
Yes: the point is a solution
No: the point is not a solution
Is (3, –5) a solution for y  3x + 4.
y  3x + 4
– 5  3(3) + 4
–5  9 + 4
–5  13
Replace x with 3 and y with 5.
This statement is true, so (3, –5) is a solution.
Is (-1, 1) a solution for y > -x + 2.
1 > -(-1) + 2
1>1+2
1>3
This statement is false, so (-1, 1) is not a solution.
Objective 2
Graph linear inequalities.
One Variable vs. Two Variables
2x  6
x3
2x  6
x3
)
3
3
When an equation in one variable is solved the answer is a point on a line.
Ax + By = C
< or > use dotted line
Ax + By < C
≤ or ≥ use solid line
To Graph Linear Inequalities
1. Graph the related equation.
 or  draw a solid line
< or > draw a dashed line
2. Test Point:
True: shade the side with the test point
False: shade the side opposite the test point
Graph: y > 4x + 1
Graph the related equation
y = 4x + 1
(0,1)
m=4
Line: > = Dotted
Test point: (0, 0)
y > 4x + 1
0 > 4(0) + 1
0 > 1 False
Shade other side of the boundary line.
Graph:
x - 4y ≥ - 8
Graph the related equation
x – 4y = -8
(0, 2) (-8, 0)
Line:
≥ = solid
Test point:
(0, 0)
0 – 0 ≥ -8 True
Graph: 3x – 4y < 0
Graph the related equation
3x – 4y = 0
(0, 0) m = 3/4
Line:
< = dotted
Test point:
(2, -2)
3(2) – 4(-2) < 0
6+8<0
False
Graph:
x≤4
Which point is a solution to the inequality
3x + 2y  12?
a) (0, 3)
b) (0, 0)
c) (2, 5)
d) (4, 5)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 13
Which point is a solution to the inequality
3x + 2y  12?
a) (0, 3)
b) (0, 0)
c) (2, 5)
d) (4, 5)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 14
Graph 2x + 3y  12.
a)
b)
c)
d)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 15
Graph 2x + 3y  12.
a)
b)
c)
d)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 16