Graphs Of Linear Inequalities Worksheet With Answers Page 4
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21The solution set is the half-plane lying on or below the line 2
−
x y
+ = .
4
***
Example 4:
Graph the inequality
x y
+ < − .
3
Solution:
We first write the inequality as an equation,
x y
+ = − . The line will be graphed as a
3
dashed line because the inequality in this problem is < , which does not include the line. We can
graph the line using x- and y-intercepts, or by putting it in slope-intercept form, y mx b
+ .
=
We will choose to find the x- and y-intercepts of
x y
+ = − .
3
x y
+ = −
3
x y
+ = −
3
x
+ = −
0
3
0
+ = −
y
3
x
= −
3
y
= −
3
A dashed line is drawn through the intercepts, which are located at ( 3, 0)
and (0, 3)
.
−
−
We now need to determine which portion of the plane should be shaded. To do this, we choose
any test point not on the line, and substitute those coordinates into the inequality to determine if
the resulting statement is true. We will choose the point (0, 0) .
x y
+ < −
3
0 0
+ < −
3
0
< −
3
Since 0
< − is not true, then (0, 0) does not satisfy the inequality, and so we shade the half-
3
plane not containing (0, 0) .
Math 1313
Page 4 of 21
Section 1.4
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