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Graphing Linear Inequalities in Two Variables ,[object Object],[object Object]
Objective- To graph inequalities on the coordinate plane. Recall… Graph  n  <   3  on a number line. - 3  - 2  - 1  0  1  2  3  4
Definitions ,[object Object],[object Object]
Some Helpful Hints ,[object Object],[object Object],[object Object],[object Object],[object Object]
Graph  y  >  3 on the coordinate plane. x y
Graph  x  - 2  on the coordinate plane. x y
[object Object],[object Object],[object Object]
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!
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 > <
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
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
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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6.6 Graphing Inequalities In Two Variables

  • 1.
  • 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.
  • 4.
  • 5. Graph y > 3 on the coordinate plane. x y
  • 6. Graph x - 2 on the coordinate plane. x y
  • 7.
  • 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