6.6 Graphing Inequalities In Two Variables

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6.6 Graphing Inequalities In Two Variables

  1. 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. 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. 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. 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. 5. Graph y > 3 on the coordinate plane. x y
  6. 6. Graph x - 2 on the coordinate plane. x y
  7. 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. 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. 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. 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. 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. 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
  13. 13. To sketch the graph of a linear inequality: <ul><li>Dashed Line </li></ul><ul><li>Like a circle on a number line, a dashed line on a coordinate plane indicates that the boundary is not part of the solution set. </li></ul><ul><li>Solid Line </li></ul><ul><li>Like a dot on a number line, a solid line on a coordinate plane indicates that the boundary is included. </li></ul>

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