6.5 ­ Linear Inequalities.notebook

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February 11, 2016

6.5: Linear Inequalities Date: 2/11

A linear inequality can be formed by replacing the equal sign in a linear equation with an inequality symbol. A solution of a linear inequality in two variables is an ordered pair that makes the inequality true. There are many solutions to linear inequalities, not just one.

Ex 1). Is the ordered pair a solution of y < x + 2?

(a) (­5, 2) (b) (4, 6)

Ex 2). Suppose an ordered pair is not a solution of y < x + 2. Must it be a solution of y > x + 2? Explain.

6.5 ­ Linear Inequalities.notebook

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The graph of a linear inequality in two variables consists of all points that represent solutions. The graph is a region called a half­plane that is bounded by a line. All points on one side of the boundary line are solutions, while all points the other side are not solutions.

Graphing Steps:

1. Write the equation in slope­intercept form: ________________“Isolate y”

2. Graph the line:

a. Use a _________________ line for _______________

b. Use a _________________ line for _______________

3. _________ the coordinates of a point in one fo the half­plane

4. _________ the half­plane containing the point if it is a _________________ of the inequality. If it is not a solution, shade the ____________ half­plane.

6.5 ­ Linear Inequalities.notebook

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Graph each of the following linear inequalities:

Ex 3). Ex 4).

6.5 ­ Linear Inequalities.notebook

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Ex 5). Ex 6).

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Ex 7). Ex 8).

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Ex 9). Suppose you can spend no more than $20 for hot dogs and hamburgers for a picnic. Hot dogs cost $5 per package, and hamburgers cost $8 per package. What are three possible combinations of packages of hamburgers and hot dogs that you could buy?

x

y

6.5 ­ Linear Inequalities.notebook

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Homework: pg. 397 #1 – 7, 8 – 30(e), 32 – 34

(graphs on graph paper)