Download Graph Linear Inequalities in Two Variables

7.8
Graph Linear Inequalities
CA Standards
in Two Variables
Alg. 6.0
Goal
Your Notes
p Graph linear inequalities in two variables.
VOCABULARY
Linear inequality in two variables The result of
replacing the 5 sign in a linear equation with
,, #, ., or $
Solution of an inequality in two variables An ordered
pair (x, y) that produces a true statement when
the values are substituted into an inequality in two
variables x and y
Graph of an inequality in two variables The set of
points that represent all solutions of the inequality
Half-plane Either half of the coordinate plane that is
divided by the boundary line of a linear inequality
Example 1
Check solutions of a linear inequality
Tell whether the ordered pair is a solution of
3x 2 4y > 9.
a. (2, 0)
b. (2, 21)
Solution
a.
3x 2 4y > 9
?
3( 2 ) 2 4( 0 ) > 9
Write inequality.
Substitute 2 for x and
0 for y.
6 >9
3
Simplify.
(2, 0) is not a solution of 3x 2 4y > 9.
b.
3x 2 4y > 9
?
3( 2 ) 2 4( 21 ) > 9
10 > 9 ✓
(2, 21)
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
is
Write inequality.
Substitute 2 for x and
21 for y.
Simplify.
a solution of 3x 2 4y > 9.
Lesson 7.8 • Algebra 1 Notetaking Guide
171
Your Notes
GRAPHING A LINEAR INEQUALITY IN TWO
VARIABLES
Step 1 Graph the boundary line. Use a dashed line
for < or >, and use a solid line for #or $.
Step 2 Test a point not on the boundary line by
checking whether the ordered pair is a solution
of the inequality.
Step 3 Shade the
half-plane
containing the
point if the ordered pair
is
a solution of
the inequality. Shade the other half-plane if
the ordered pair is not a solution.
Graph a linear inequality in two variables
Example 2
1
Graph the inequality y < 2}
x 1 4.
2
Solution
1
Step 1
x 1 4. The inequality
Graph the equation y 5 2}
2
is <, so use a dashed line.
Step 2
Test (0, 0) in y < 2}
x 1 4.
2
1
1
( 0 )14
0 < 2}
2
0 < 4 ✓
Step 3
Shade the half-plane that contains (0, 0)
because (0, 0) is a solution of the inequality.
10
y
6
2
22
22
2
6
10
x
26
172
Lesson 7.8 • Algebra 1 Notetaking Guide
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Your Notes
Graph a linear inequality in one variable
Example 3
Graph the inequality x $ 4.
Solution
Step 1 Graph the equation x 5 4. The inequality is $,
so use a solid line.
Step 2
Test (0, 3) in x $ 4. You only substitute the
x-coordinate because the inequality does
not have the variable y .
0 $43
Step 3
Shade the half-plane that does not contain
(0, 3), because (0, 3) is not a solution of the
inequality.
y
3
1
1
21
21
3
x
5
23
Guided Practice Graph the inequality.
1. 2y 1 4x > 8
5
2. y < 2
y
y
3
3
1
1
23
21
21
23
1
3
5 x
21
21
1
3
x
23
Homework
23
Copyright © by McDougal Littell, a division of Houghton Mifflin Company.
Lesson 7.8 • Algebra 1 Notetaking Guide
173