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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.
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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.
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Graph each of the following linear inequalities:
Ex 3). Ex 4).
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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
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Homework: pg. 397 #1 – 7, 8 – 30(e), 32 – 34
(graphs on graph paper)