Section 2.8- Two-Variable Inequalities
Essential Question: How are two-variable inequalities different than one-variable
inequalities?
Do Now:
How many of each can you buy?
Is there one than one possible combination to spend your money?
Graphing Inequalities in Two Variables

Similar to graphing a ___________

Separated by a “_______________ ________”

Separates the coordinate into two _________-__________
o Consists of the solutions of the inequality

May or may not include points on the line

Use _______ point that is ________ on boundary to check answer
NOTE: Dashed vs. Solid Boundary Lines
Why are they drawn like that?
Example 1: What is the graph of each inequality?
a. 𝑦 > 3𝑥 − 1
b. 𝑦 ≤ 3𝑥 − 1
Solid or dashed boundary?
Use test point:
Solid or dashed boundary?
Use test point:
Example 2: What is the graph of each inequality?
a. 𝑦 ≤ −2𝑥 + 1
b. 𝑦 > −2𝑥 + 1
Solid or dashed boundary?
Use test point:
Solid or dashed boundary?
Use test point:
Example 3: Using a Linear Inequality
a.
Write an inequality to represent how many rides you can go on.
Graph your solution from part a.
Why only include answers in quadrant I?
b. Suppose that you decide to spend no
more than $30 for tickets. What are the
possible combinations of small and large
rides that you can ride now?
Example 4: What is the graph of 1 − 𝑦 <
|𝑥 + 2|?
Example 5: Graph the inequality.
𝑦 − 4 ≥ 2|𝑥 − 1|
What do we need to do first?
Graph the inequality.
Using the Graphing Calculator to Check Answer
> 𝑜𝑟 ≥
1. Input function in the Y= menu.
2. Scroll to the far left of your equation.
< 𝑜𝑟 ≤
1. Input function in the Y= menu.
2. Scroll to the far left of your equation.
3. Press enter until this icon
up. This means to shade above.
3. Press enter until this icon
This means to shade below.
pops
pops up.
Summary of Graphing Inequalities
Inequality Sign
Solid or Dashed
Boundary?
<
≤
>
Shading
Solutions on
Boundary Line
included?
HW: p. 118-120 #9-17 odds, 22-26 evens, 27, 28, 30, 31, 34, 45, 46, 52-55
≥