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**2.6 Linear Inequalities in Two Variables**

Algebra 2 2.6 Linear Inequalities in Two Variables

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**Warm-up Graph the following lines on the same coordinate plane. y = 2**

x = -1 -x + y = 1 y = 3x + 1

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**Learning Targets Students should be able to…**

Graph Linear Inequalities in two variables Use linear inequalities to solve real life problems

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

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**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)

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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.

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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

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**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

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

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**Example 3: Two Variables**

c) y < -2x d) 2x – 5y ≥ 10

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**Example 3: Two Variables**

e) y ≤ 4x f) 4x – 2y ≥ 8

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**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.

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**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.

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**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.

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**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

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**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

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Closure

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

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