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Graph each inequality on a number line. 1. x > –5 2. y ≤ 0 3. Write –6x + 2y = –4 in slope-intercept form, and graph. y = 3x – 2 Warm-Up

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Inequalities

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Learning Targets Review Inequalities Review Inequalities Graphing Inequalities Graphing Inequalities Knowing where Possible Solutions Exist Knowing where Possible Solutions Exist Testing for Possible Solutions Testing for Possible Solutions

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What is an Inequality? Definition: two expressions are not equal to one another. Definition: two expressions are not equal to one another.

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Equality vs. Inequality

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Number Lines Equalities on a number line: Equalities on a number line: Inequalities on a number line: -1 0 1

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Graphically Equalities on a coordinate plane: Equalities on a coordinate plane: Inequalities on a coordinate plane:

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Different Symbols… Different Lines/Points Solid Line, Filled Point Dashed Line, Hollow Point

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Objective - To graph linear inequalities in the coordinate plane. Number LineCoordinate Plane -4 -3 -2 -1 0 1 2 3 4 y x x = 3

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Number LineCoordinate Plane -4 -3 -2 -1 0 1 2 3 4 y x y = -2

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Boundary Line Test a Point False! y x

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y x Solid line If y = mx + b,

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Why do we flip the sign? Pause and Ponder…

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y x Dashed line If y = mx + b,

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y x Solid line If y = mx + b,

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y x Dashed line If y = mx + b, Write the inequality described by the graph below. -4 +3+3

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Determine whether the given point is a solution to the inequality -2x + 3y < 9. 1) (2, -3) Yes, (2,-3) is a solution. 2) (3, 5) No, (3,5) is not a solution.

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Problem If you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have. Let n = # of nickels Let d = # of dimes 0.05 n + 0.10 d < 5.00 or 5 n + 10 d < 500

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nd 0 50 1000 0 10 20 30 40 50 60 70 80 90 100 n d 60 50 40 30 20 10 0

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Graph both inequalities over each other: Therefore our answer lies in the combined shaded region:

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Non linear Inequalities

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Non Linear Inequalities In chapter 4 we studied parent graphs and their transformation. In chapter 4 we studied parent graphs and their transformation. In the next few slides you will be given non linear graphs. Use your knowledge of parent graphs to display a graph for each function. In the next few slides you will be given non linear graphs. Use your knowledge of parent graphs to display a graph for each function. Then use a test point to graph the inequalities that follow. Then use a test point to graph the inequalities that follow.

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On your own: Review your notes. Rewrite and fortify them if needed. Review your notes. Rewrite and fortify them if needed. Update your vocab list, if needed. Update your vocab list, if needed.

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