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6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
6.6 Graphing Inequalities In Two Variables
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6.6 Graphing Inequalities In Two Variables

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  • 1. Graphing Linear Inequalities in Two Variables <ul><li>Goal 1: Graph a linear inequality in two variables </li></ul><ul><li>Goal 2: Model a real life situation with a linear inequality. </li></ul>
  • 2. Objective- To graph inequalities on the coordinate plane. Recall… Graph n < 3 on a number line. - 3 - 2 - 1 0 1 2 3 4
  • 3. Definitions <ul><li>Half-plane: The region of a graph on one side of a boundary. </li></ul><ul><li>Boundary: A boundary of an inequality is a line that separates the coordinate plane into half-planes. </li></ul>
  • 4. Some Helpful Hints <ul><li>If the sign is > or < the line is dashed </li></ul><ul><li>If the sign is  or  the line will be solid </li></ul><ul><li>When dealing with just x and y. </li></ul><ul><li>If the sign > or  the shading either goes up or to the right </li></ul><ul><li>If the sign is < or  the shading either goes down or to the left </li></ul>
  • 5. Graph y > 3 on the coordinate plane. x y
  • 6. Graph x - 2 on the coordinate plane. x y
  • 7. <ul><li>When dealing with slanted lines </li></ul><ul><li>If it is > or  then you shade above </li></ul><ul><li>If it is < or  then you shade below the line </li></ul>
  • 8. Graph y - 3x + 2 on the coordinate plane. x y Boundary Line y = - 3x + 2 m = - 3 b = 2 Test a point not on the line test (0,0) 0 -3(0) + 2 Not true!
  • 9. Graph y - 3x + 2 on the coordinate plane. x y Instead of testing a point If in y = mx + b form... Shade up Shade down Solid line Dashed line > <
  • 10. Graph on the coordinate plane. 3x - 4y > 12 - 3x - 3x - 4y > - 3x + 12 - 4 - 4 y < x - 3 m = b = - 3 Boundary Line x y
  • 11. 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
  • 12. 5n + 10d < 500 n d 0 50 100 0 0 10 20 30 40 50 60 70 80 90 100 n d 60 50 40 30 20 10 0

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