Page 35 - Math Course 3 (Book 1)

Graphing Linear Inequalities
Mo. 1

Lesson 7 Key Concept

KEY CONCEPTS: Half-Plane and Bounderies
1. Graph inequalities on the coordinate plane. Words Any line in the plane divides the plane
2. Solve real-world problems involving linear into two regions called half-planes. The
inequalities. line is called the boundary of each of the
two half-planes.
Model y
MO. 1 - L7a Half-Plane
Graphing Inequalities with Boundary

Variables 0 x

Half-Plane
Vocabulary A-Z

Let us learn some vocabulary

Let’s Begin

half-plane
The graph of the solution set of ordered pairs for
an inequality fill a region on the coordinate plane Graph an Inequality
called a half-plane.
Example

y
Half-Plane Graph 2y – 4x > 6.

Step 1 Solve for y in terms of x.
0 x

Half-Plane 2y – 4x > 6 Original inequality

2y – 4x + 4x > 6 + 4x Add 4x to each side.

2y > 4x + 6 Simplify.
boundary
2y –4x + 6
An equation defines the boundary or edge for each 2 > 2 Divide each side by 2.
half-plane.
y > 2x + 3 Simplify.

y

Boundary Step 2 Graph y = 2x + 3.

0 x Since y > 2x +3 does not include values when
y = 2x + 3, the boundary is not included in the
solution set. The boundary should be drawn as a
dashed line.

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