Graphs Of Linear Inequalities Worksheet With Answers Page 3
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21We will choose to find the x- and y-intercepts of 2
−
x y
+ = .
4
−
2
x y
+ =
4
−
2
x y
+ =
4
( )
−
2
x
+ =
0 4
−
2 0
+
4
2
x
4
y
4
−
=
=
x
= −
2
A solid line is drawn through the intercepts, which are located at ( 2, 0)
−
and (0, 4) .
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) .
2
x y
4
−
+ ≤
?
( )
−
2 0
+ ≤
0 4
0 4
≤
Since 0 4
≤
is true, then (0, 0) satisfies the inequality, and so we shade the half-plane containing
(0, 0) .
Math 1313
Page 3 of 21
Section 1.4
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