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(Sections 7.5-7.6: Graphing Inequalities and Linear Programming)
7.36
SECTION 7.5: GRAPHING INEQUALITIES, and
SECTION 7.6: LINEAR PROGRAMMING
In
Example 2 on p.542
, the one-variable linear inequalities
x
>
−
2
and
y
≤
3
are graphed in the
xy
-plane.
In
Example 3 on p.542
, the two-variable linear inequality
x
−
y
<
2
is graphed in the
xy
-plane.
Two methods:
Method 1: Test Point Method
Step 1:
Graph the boundary line, which separates the
xy
-plane into two half-
planes.
• Replace the inequality symbol with “=” to obtain the equation of the
boundary line.
• To figure out how to graph the line,
§ Put the equation in slope-intercept form:
y
=
mx
+
b
, or
§ Plot the intercepts. (See
Section 1.3:
Notes 1.16-1.17
.)
•
If the inequality had
Then graph the line as
≤
or
≥
(weak inequality)
a solid line
(We include the line in the graph.)
<
or
>
(strict inequality)
a dashed line
(We exclude the line.)
Step 2:
Decide which half-plane to shade.
• Pick a test point not on the boundary line.
0,0
( )
is usually the best choice
if it doesn't lie on the line.
• If the coordinates of the test point make the inequality true, shade the
half-plane containing the test point (i.e., shade “towards” the test point).
Otherwise, shade the other half-plane (i.e., shade “away from” the test
point).

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(Sections 7.5-7.6: Graphing Inequalities and Linear Programming)
7.37
Method 2: "Solve for
y
" Method
Step 1:
Put the inequality in the form

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