1. 2.6 Linear Inequalities In two Variables
Algebra 2

2. Definitions
Linear Inequality: an inequality that can be Witten in one of the following forms
𝐴𝑥+𝐵𝑦<𝐶
𝐴𝑥+𝐵𝑦≤𝐶
𝐴𝑥+𝐵𝑦>𝐶
𝐴𝑥+𝐵𝑦≥𝐶
Solution of a linear inequality: The values of x and y that make the inequality true

3. Example Check whether the ordered pair is a solution of 4𝑥−2𝑦≥8.
(3, 3)
(-2, -9)
Check whether the ordered pair is a solution of 3𝑥−𝑦≤6.
(2, 0)
(-1, 10)

4. Investigating the Graph of an Inequality
Graph the following points (0, 0), (0, 2), (0, 4), (-2, 0), (-2, 2), (-2, 4), (-4, 0), (-4, 2), (- 4, 4), (-2, -2), (-4, -2), (-2, -4), (-4, -4), (0, - 2), (0, -4), (2, 0), (4, 0), (2, 2), (2, 4). (4, 2), (4, 4), (2, -2), (2, -4), (4, -2), and (-4, -4)
Test each circled point to see whether it is a solution of 𝑥+𝑦≥1. If t is a solution, color it blue. If it is not a solution, color it red.
Graph the line 𝑥+𝑦=1. What relationship do you see between the colored points and the line?

5. Investigating the Graph of an Inequality
Describe a general strategy for graphing an inequality in two variables
Graphing A Linear Inequality
1) Graph the boundary line of the inequality. Use a dashed line for < or > and a solid line for ≤ or ≥
2) To decide which side of the boundary to shade, test a point no on the boundary line to see whether it is a solution of the inequality. Then shade the appropriate half-plane

6. Examples Graph the following inequalities 𝑦≥2 𝑥>−1 4𝑥+2𝑦≥8
3𝑥−𝑦<3

7. Example
You have $200 to spend on CDs and music videos. CDs cost $10 and music videos cost $15.
Write a linear inequality in two variables to represent the number of CDs x and music videos y you can buy.
Graph the inequality. Give three possible combinations of the number of CDs and music videos you can buy.

8. Example
You have $15 for fresh fruit for a salad. Write a linear inequality in two variables for how many pound of strawberries x at $1.25 per pound and cherries y at $2.40 per pound you can buy. What are the intercepts of the graph?