Graphs Of Linear Inequalities Worksheet With Answers Page 19
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21Example 13:
Write the system of inequalities that corresponds to the following graph.
Solution:
First, we need to find the equation of each line. We will use the slope and y-intercept,
and write each line in the form y mx b
=
+ .
(
)
(
)
Line 1 passes through the point
0, 9 , so
b = . Since the line also passes through
9
0.5, 0 ,
y
−
y
0 9
−
−
9
−
9 2
2
1
m
=
=
=
=
⋅ = −
18
.
1
x
−
x
0.5 0
−
1 1
2
1
2
The equation for Line 1 is
y
= −
18
x
+ .
9
The equation for Line 2 is
y = .
9
The equation for Line 3 is
x = .
3
The equation for Line 4 is
y = − .
2
We now need to determine the inequalities:
The shaded region lies above Line 1 and the line is solid, so
y
≥ −
18
x
+ .
9
The shaded region lies below Line 2 and the line is dashed, so
y < .
9
The shaded region lies to the left of Line 3 and the line is dashed, so
x < .
3
The shaded region lies above Line 4 and the line is solid, so
y ≥ − .
2
We can combine the inequalities for Line 2 and Line 4: 2
− ≤ <
y
9
Math 1313
Page 19 of 21
Section 1.4
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