Graphs Of Linear Inequalities Worksheet With Answers Page 6
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21We will choose to find the x- and y-intercepts of
y
=
3
x
+ .
6
y
=
3
x
+
6
y
=
3
x
+
6
( )
0 3
=
x
+
6
y
=
3 0
+
6
3
x
6
y
6
−
=
=
x
= −
2
A solid line is drawn through the intercepts, which are located at ( 2, 0)
−
and (0, 6) .
We can now use our shortcut rather than selecting a test point. Since the inequality is of the form
y
≥
3
x
+ , we shade above the line.
6
The solution set is the half-plane lying on or above the line
y
=
3
x
+ .
6
***
Example 6:
Graph the inequality 12
3
> − .
9
−
x
−
y
Solution:
We first write the inequality as an equation, 12
−
x
−
3
y
= − . The line will be graphed
9
as a 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 using the slope and y-intercept from slope-
intercept form.
Math 1313
Page 6 of 21
Section 1.4
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