Graphing Linear Inequalities in
Two Variables
Section 2.8
Review
Which of the following ordered pairs is a solution of 2x + 5y
>9?
A)
B)
C)
D)
(–4, –1)
(–2, 3)
(2, –4)
(6, –1)
 2,3
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Steps in Graphing
A. Draw the graph either applying slope–intercept or
quick graph form
1. When using “cover–up,” if there is a negative
coefficient in the y, flip the direction of the
graph
B. Determine what the sign is and graph the line
1. Dotted Line: Greater, Less, or not–equal to
2. Solid Line: Greater then OR equal to, Less than
OR equal to, Equal to
C. Shade above or below the line by looking at
inequality
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2.8: Graph Linear Inequalities in Two Variables
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Steps in Graphing
Greater Than
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2.8: Graph Linear Inequalities in Two Variables
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Steps in Graphing
Less Than
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Example 1
Graph 2x + 3y < 6
Graph, as if, it was an equality.
3 y  2 x  6
2
y   x2
3
OR
(3, 0)
and
(0, 2)
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Example 2
Graph –4x – 2y > 8
2 y  4 x  8
2 y 4 x  8

2
2
y  2 x  4
OR
(–2, 0)
and
(0, –4)
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Example 2 Calculator
Graph –4x – 2y > 8
y  2 x  4
Must be in slope–intercept form
Go to Y= in graphing calculator
Greater than
Less than
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Example 2 Calculator
Graph –4x – 2y > 8
y  2 x  4
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Example 3
Graph y > 4
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Example 4
Graph x < 7
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Your Turn
Graph 3 > 3/2y
y<2
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Example 5
Graph 2/3 (2x – y) < 2
y > 2x – 3
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Example 6
x  1st job
y  2nd job
9 x  12 y  240
 25,0
 0, 20
$12 an hour job (every 5)
You have two part–time summer jobs, one that pays $9 and
hour and another that pays $12 an hour. You would like to
earn at least $240 a week. Write an inequality describing the
possible amounts of times you can schedule at each jobs.
Graph the inequality. Each space is worth 5.
$9 an hour job (every 5)
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Your Turn
x  small pizza
y  large pizza
12 x  18 y  4800
 400,0
 0, 266.67 
Large Pizzas (per 50)
A pizza place has 4800 ounces (300 pounds) of dough. A small
pizza uses 12 ounces of dough and a large pizza uses 18
ounces of dough. Write and graph an inequality describing
the possible numbers of small and large pizzas that can be
made. Each space is worth 50.
Small Pizzas (per 50)
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Assignment
Page 135
3–27 odd, 43–47 odd
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