Graphs Of Linear Inequalities Worksheet With Answers Page 13
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21We now write the second inequality, 3
−
x y
− ≥ , as an equation, 3
3
−
x y
− = . The line will be
3
graphed as a solid line because the inequality is ≥ , which includes the line. We will graph the
line using x- and y-intercepts.
−
3
x y
− = −
3
−
3
x y
− =
3
( )
−
3
x
− =
0 3
−
3 0
− =
y
3
−
3
x
=
3
− =
y
3
x
= −
1
y
= −
3
(
)
(
)
A solid line is drawn through the intercepts, which are located at
−
1, 0
and
0, 3
−
.
We then need to decide whether to shade above or below the line. Instead of choosing a test
point, we can isolate the variable y on the left-hand side of 3
−
x y
− ≥
3
and determine which
half-plane to shade. (Remember that when dividing by a negative number, we need to reverse the
inequality.)
3
3
−
x y
− ≥
− ≥
y
3
x
+
3
y
≤ −
3
x
−
3
Since the inequality is of the form
y
≤ −
3
x
− , we shade below the line, shown in the colors
3
aqua and green below. (The green region is where the aqua shading overlaps with the previous
yellow shading.)
Math 1313
Page 13 of 21
Section 1.4
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