# 2.6 Linear Inequalities in Two Variables

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2.6 Linear Inequalities in Two Variables
Algebra 2 2.6 Linear Inequalities in Two Variables

Warm-up Graph the following lines on the same coordinate plane. y = 2
x = -1 -x + y = 1 y = 3x + 1

Learning Targets Students should be able to…
Graph Linear Inequalities in two variables Use linear inequalities to solve real life problems

Homework Check Section 2.5 Page 103 – 105 # 6 – 12, 24, 25

Example 1: Checking Solutions of Inequalities
Check whether the given ordered pair is a solution of 4x – 2y > 8 a) (-2, 3) b) (-2, -9) c) (4, 4)

Vocabulary - The graph of linear inequalities is the graph of all solutions of the inequality. - Solution: when (x , y) is substituted into the inequality and the statement is true. - Boundary line: divides the coordinate plane into 2 half-planes: a shaded region which contains the points that are solutions, and an unshaded region which contains the points that are not solutions.

Rules for Graphing Do the exact same thing as graphing a line, until the very end. 1. Boundary Line: < or > include the boundary – closed circle or solid line ( ) < or > do not include the boundary – open circle or dashed line ( ) 1 variable, x = means vertical line, y = means a horizontal line

Rules for Graphing 2. Side to shade:
Make sure that your isolated variable is on the left side. < or ≤ shade below the line > or ≥ shade above the line If it is a vertical line < or ≤ shade to the left of the line > or ≥ shade to the right of the line

Example 2: One Variable a) y < b) x ≤ 1

Example 3: Two Variables
c) y < -2x d) 2x – 5y ≥ 10

Example 3: Two Variables
e) y ≤ 4x f) 4x – 2y ≥ 8

Example 4: Writing and Using a Linear Inequality
You have \$200 to spend on CDs and music videos. CDs cost \$10 each and music videos cost \$15. a. Write a linear inequality in two variables to represent the number of CDs x and music videos y you can buy.

Writing and Using a Linear Inequality
You have \$200 to spend on CDs and music videos. CDs cost \$10 each and music videos cost \$15.

Writing and Using a Linear Inequality
You have \$200 to spend on CDs and music videos. CDs cost \$10 each and music videos cost \$15. b. Graph the inequality and discuss three possible solutions in the context of the real-life situation.

Writing and Using a Linear Inequality
b. Graph the inequality and discuss three possible solutions in the context of the real-life situation. 10x + 15y ≤ 200 Answers drawn on next slide

Writing and Using a Linear Inequality
b. Graph the inequality and discuss three possible solutions in the context of the real-life situation. 10x + 15y ≤ 200

Closure

Homework Page 111 – 112 #15, 16, 20, 21, 24 – 26, 36 – 44 even