Name: _________________________________________________ Date: _______________ Period: ________
Algebra 2
Section 2-8
Two Variable Inequalities
Linear Inequality: _________________________________________________________________________
_________________________________________________________________________________________.
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The __________________ of the graph separates the coordinate plane into two
_________________, one of which consists of solutions of the inequality.
Half- plane
Boundary
Steps to graphing an Inequality
1. Solve the inequality for 𝑦.
2. Graph the boundary line.

Solid boundary line: ____________________

Dashed boundary line: __________________
3. Choose a test point (0, 0). Substitute 𝑥 = 0 and 𝑦 = 0 into your inequality.

If it is ______________, shade the half plane that includes (0,0).

If it is ______________, shade the half plane that does not include (0,0).
Example:
1. 𝑦 > 3𝑥 − 1
2. 5𝑥 − 2𝑦 ≥ −10
Try these:
1. 3(𝑥 − 2) + 2𝑦 ≤ 6
2.
3
4
2
5
𝑥 + 3𝑦 > 2
Graphing an Absolute Value Inequality
*Follow the same directions for graphing a linear inequality. You graph will be V-shaped instead of a line.
Example:
1 − 𝑦 < |𝑥 + 2|
Vertex: ____________
Axis: _____________
Reflection: ____________
Try these:
1. |𝑥 − 1| > 𝑦 + 7
2. 𝑦 − |𝑥| ≤ 21
Writing an Inequality based on a graph
Recall: 𝑦 = |𝑥| is the parent graph
Vertex: _____________________
Translated: __________________
Reflected: ___________________
Equation: ______________________
Try these:
Directions: Write the equation of the inequality shown on the graph.
1.
2.
Important tips to remember when graphing Inequalities:



Solid line for ≤, ≥
Dashed line for <, >
Pick a test point to decide where to shade: (0,0) is a good point to use
- If it is true: shade in that region
- If it is false: shade it the opposite region