Linear Inequalities Worksheets Page 36
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50Graphing Inequalities
Graphing Inequalities
in Two Variables
in Two Variables
Then
Now
Why?
You graphed
1
Graph linear
Hannah has budgeted $35
linear equations.
inequalities on the
every three months for car
(Lesson 3-1)
coordinate plane.
maintenance. From this she
must buy oil costing $3 and
2
Solve inequalities by
filters that cost $7 each.
graphing.
How much oil and how many
filters can Hannah buy and
stay within her budget?
y
New
Vocabulary
1
Graph Linear Inequalities
The graph of a linear
boundary
inequality is the set of points that represent all of the
Half-Plane
half-plane
possible solutions of that inequality. An equation defines a
Boundary
closed half-plane
boundary, which divides the coordinate plane into two
open half-plane
x
half-planes.
Half-Plane
The boundary may or may not be included in the graph.
When it is included, the solution is a closed half-plane.
When not included, the solution is an open half-plane.
Tennessee
Curriculum Standards
Key
Concept
Graphing Linear Inequalities
CLE 3102.3.4 Solve
problems involving linear
equations and linear
Step 1
Graph the boundary. Use a solid line when the inequality contains ≤ or ≥.
inequalities.
Use a dashed line when the inequality contains < or >.
3102.3.26 Graph linear
inequalities on the coordinate
Step 2
Use a test point to determine which half-plane should be shaded.
plane and identify regions of
the graph containing ordered
Step 3
Shade the half-plane that contains the solution.
pairs in the solution.
SPI 3102.3.5 Write and/or
solve linear equations,
inequalities, and compound
Example 1
Graph an Inequality (< or >)
inequalities including those
containing absolute value.
Graph 3x - y < 2.
Step 1
First, solve for y in terms of x.
3x - y < 2
-y < -3x + 2
y > 3x - 2
Then, graph y = 3x - 2. Because the inequality involves >, graph
the boundary with a dashed line.
y
Step 2
y = 3x - 2
Select (0, 0) as a test point.
-
< 2
3x
y
Original inequality
3(0)
-
0
< 2
x = 0 and y = 0
( 0, 0 )
0 < 2
true
x
Step 3
So, the half-plane containing the origin is the
solution. Shade this half-plane.
GuidedPractice
Graph each inequality.
_
1
1A. y >
x + 3
1B. x - 1 > y
2
315
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