SECTION 6-4
              Write and Graph Linear Inequalities




Tue, Dec 01
ESSENTIAL QUESTIONS

              How do you write linear inequalities in two variables?

              How do you graph ...
VOCABULARY

        1. Open Half-plane:

       2. Boundary:
       3. Linear Inequality:

       4. Solution to the Inequ...
VOCABULARY

        1. Open Half-plane: A dashed boundary line separates
           the plane
       2. Boundary:
       3...
VOCABULARY

        1. Open Half-plane: A dashed boundary line separates
           the plane
       2. Boundary: The line...
VOCABULARY

        1. Open Half-plane: A dashed boundary line separates
           the plane
       2. Boundary: The line...
VOCABULARY

        1. Open Half-plane: A dashed boundary line separates
           the plane
       2. Boundary: The line...
VOCABULARY

       5. Graph of the Inequality:



       6. Closed Half-plane:

       7.Test Point:




Tue, Dec 01
VOCABULARY

       5. Graph of the Inequality: Includes graphing the
           boundary line and the shaded half-plane th...
VOCABULARY

       5. Graph of the Inequality: Includes graphing the
           boundary line and the shaded half-plane th...
VOCABULARY

       5. Graph of the Inequality: Includes graphing the
           boundary line and the shaded half-plane th...
GRAPHING A LINEAR
                 INEQUALITY




Tue, Dec 01
GRAPHING A LINEAR
                       INEQUALITY
              Begin by treating the inequality as an equation to
     ...
GRAPHING A LINEAR
                       INEQUALITY
              Begin by treating the inequality as an equation to
     ...
GRAPHING A LINEAR
                       INEQUALITY
              Begin by treating the inequality as an equation to
     ...
GRAPHING A LINEAR
                       INEQUALITY
              Begin by treating the inequality as an equation to
     ...
GRAPHING A LINEAR
                       INEQUALITY
              Begin by treating the inequality as an equation to
     ...
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 1

                Tell whether the given coordinates satisfy each
              inequality by testing each point....
EXAMPLE 2

                  Graph the following inequalities.
              a. y > 3x − 5




Tue, Dec 01
EXAMPLE 2

                    Graph the following inequalities.
               a. y > 3x − 5

              m=3




Tue, ...
EXAMPLE 2

                    Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3, ...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                     Graph the following inequalities.
                a. y > 3x − 5

              m = 3 Up 3,...
EXAMPLE 2

                    Graph the following inequalities.
                      3
              b. y ≤ − x + 4
    ...
EXAMPLE 2

                  Graph the following inequalities.
                    3
            b. y ≤ − x + 4
          ...
EXAMPLE 2

                    Graph the following inequalities.
                      3
              b. y ≤ − x + 4
    ...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
EXAMPLE 2

                     Graph the following inequalities.
                         3
              b. y ≤ − x + 4
...
WHERE TO SHADE




Tue, Dec 01
WHERE TO SHADE


              When y is isolated, there is a trick we can use:




Tue, Dec 01
WHERE TO SHADE


              When y is isolated, there is a trick we can use:

        y goes down when we get less (<, ...
WHERE TO SHADE


               When y is isolated, there is a trick we can use:

        y goes down when we get less (<,...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              Rectangle ABCD has a perimeter of at least 10 cm.
     a. Write a linear inequality that represen...
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

              b. Graph the solution to the inequality.
                            y ≥ −x + 5




Tue, Dec 01
EXAMPLE 3

      c. Does the “trick” tell us to shade above or below the
                boundary line? How do you know?

...
EXAMPLE 3

      c. Does the “trick” tell us to shade above or below the
                boundary line? How do you know?

...
EXAMPLE 3

      c. Does the “trick” tell us to shade above or below the
                boundary line? How do you know?

...
HOMEWORK




Tue, Dec 01
HOMEWORK



                             p. 260 #1-37 odd




              “Everyone has talent. What is rare is the cour...
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Integrated 2 Section 6-4

  1. 1. SECTION 6-4 Write and Graph Linear Inequalities Tue, Dec 01
  2. 2. ESSENTIAL QUESTIONS How do you write linear inequalities in two variables? How do you graph linear inequalities in two variables on the coordinate plane? Where you’ll see this: Business, market research, inventory Tue, Dec 01
  3. 3. VOCABULARY 1. Open Half-plane: 2. Boundary: 3. Linear Inequality: 4. Solution to the Inequality: Tue, Dec 01
  4. 4. VOCABULARY 1. Open Half-plane: A dashed boundary line separates the plane 2. Boundary: 3. Linear Inequality: 4. Solution to the Inequality: Tue, Dec 01
  5. 5. VOCABULARY 1. Open Half-plane: A dashed boundary line separates the plane 2. Boundary: The line that separates half-planes 3. Linear Inequality: 4. Solution to the Inequality: Tue, Dec 01
  6. 6. VOCABULARY 1. Open Half-plane: A dashed boundary line separates the plane 2. Boundary: The line that separates half-planes 3. Linear Inequality: A sentence where instead of an = sign, we use <, >, ≤, ≥, or ≠ 4. Solution to the Inequality: Tue, Dec 01
  7. 7. VOCABULARY 1. Open Half-plane: A dashed boundary line separates the plane 2. Boundary: The line that separates half-planes 3. Linear Inequality: A sentence where instead of an = sign, we use <, >, ≤, ≥, or ≠ 4. Solution to the Inequality: ANY ordered pair that makes the inequality true Tue, Dec 01
  8. 8. VOCABULARY 5. Graph of the Inequality: 6. Closed Half-plane: 7.Test Point: Tue, Dec 01
  9. 9. VOCABULARY 5. Graph of the Inequality: Includes graphing the boundary line and the shaded half-plane that includes the solution 6. Closed Half-plane: 7.Test Point: Tue, Dec 01
  10. 10. VOCABULARY 5. Graph of the Inequality: Includes graphing the boundary line and the shaded half-plane that includes the solution 6. Closed Half-plane: A solid boundary line separates the plane 7.Test Point: Tue, Dec 01
  11. 11. VOCABULARY 5. Graph of the Inequality: Includes graphing the boundary line and the shaded half-plane that includes the solution 6. Closed Half-plane: A solid boundary line separates the plane 7.Test Point: A point NOT on the boundary line that is used to test whether to shade above or below the boundary line Tue, Dec 01
  12. 12. GRAPHING A LINEAR INEQUALITY Tue, Dec 01
  13. 13. GRAPHING A LINEAR INEQUALITY Begin by treating the inequality as an equation to graph the boundary line and isolate y. Tue, Dec 01
  14. 14. GRAPHING A LINEAR INEQUALITY Begin by treating the inequality as an equation to graph the boundary line and isolate y. If <, >, or ≠, the boundary line will be dashed. Tue, Dec 01
  15. 15. GRAPHING A LINEAR INEQUALITY Begin by treating the inequality as an equation to graph the boundary line and isolate y. If <, >, or ≠, the boundary line will be dashed. If ≤ or ≥, the boundary line will be solid. Tue, Dec 01
  16. 16. GRAPHING A LINEAR INEQUALITY Begin by treating the inequality as an equation to graph the boundary line and isolate y. If <, >, or ≠, the boundary line will be dashed. If ≤ or ≥, the boundary line will be solid. Use a test point to determine shading OR Tue, Dec 01
  17. 17. GRAPHING A LINEAR INEQUALITY Begin by treating the inequality as an equation to graph the boundary line and isolate y. If <, >, or ≠, the boundary line will be dashed. If ≤ or ≥, the boundary line will be solid. Use a test point to determine shading OR If y is isolated, < and ≤ shade below, > and ≥ shade above Tue, Dec 01
  18. 18. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 (3, 5), (4, 0) Tue, Dec 01
  19. 19. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 (3, 5), (4, 0) 2(3) − 3(5) < 0 Tue, Dec 01
  20. 20. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 (3, 5), (4, 0) 2(3) − 3(5) < 0 6 −15 < 0 Tue, Dec 01
  21. 21. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 (3, 5), (4, 0) 2(3) − 3(5) < 0 6 −15 < 0 −9 < 0 Tue, Dec 01
  22. 22. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 (3, 5), (4, 0) 2(3) − 3(5) < 0 6 −15 < 0 −9 < 0 (3, 5) is a solution Tue, Dec 01
  23. 23. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 2(4) − 3(0) < 0 (3, 5), (4, 0) 2(3) − 3(5) < 0 6 −15 < 0 −9 < 0 (3, 5) is a solution Tue, Dec 01
  24. 24. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 2(4) − 3(0) < 0 (3, 5), (4, 0) 8−0<0 2(3) − 3(5) < 0 6 −15 < 0 −9 < 0 (3, 5) is a solution Tue, Dec 01
  25. 25. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 2(4) − 3(0) < 0 (3, 5), (4, 0) 8−0<0 2(3) − 3(5) < 0 8<0 6 −15 < 0 −9 < 0 (3, 5) is a solution Tue, Dec 01
  26. 26. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 2(4) − 3(0) < 0 (3, 5), (4, 0) 8−0<0 2(3) − 3(5) < 0 8<0 6 −15 < 0 (4, 0) is not a solution −9 < 0 (3, 5) is a solution Tue, Dec 01
  27. 27. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? a. 2x − 3y < 0 2(4) − 3(0) < 0 (3, 5), (4, 0) 8−0<0 2(3) − 3(5) < 0 8<0 6 −15 < 0 (4, 0) is not a solution −9 < 0 The boundary line is dashed (3, 5) is a solution Tue, Dec 01
  28. 28. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 (-2, -6), (0, 0) Tue, Dec 01
  29. 29. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 (-2, -6), (0, 0) 4(−6) − (−2) ≥ −6 Tue, Dec 01
  30. 30. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 (-2, -6), (0, 0) 4(−6) − (−2) ≥ −6 −24 + 2 ≥ −6 Tue, Dec 01
  31. 31. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 (-2, -6), (0, 0) 4(−6) − (−2) ≥ −6 −24 + 2 ≥ −6 −22 ≥ −6 Tue, Dec 01
  32. 32. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 (-2, -6), (0, 0) 4(−6) − (−2) ≥ −6 −24 + 2 ≥ −6 −22 ≥ −6 (-2, -6) is not a solution Tue, Dec 01
  33. 33. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 4(0) − 0 ≥ −6 (-2, -6), (0, 0) 4(−6) − (−2) ≥ −6 −24 + 2 ≥ −6 −22 ≥ −6 (-2, -6) is not a solution Tue, Dec 01
  34. 34. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 4(0) − 0 ≥ −6 (-2, -6), (0, 0) 0 − 0 ≥ −6 4(−6) − (−2) ≥ −6 −24 + 2 ≥ −6 −22 ≥ −6 (-2, -6) is not a solution Tue, Dec 01
  35. 35. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 4(0) − 0 ≥ −6 (-2, -6), (0, 0) 0 − 0 ≥ −6 4(−6) − (−2) ≥ −6 0 ≥ −6 −24 + 2 ≥ −6 −22 ≥ −6 (-2, -6) is not a solution Tue, Dec 01
  36. 36. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 4(0) − 0 ≥ −6 (-2, -6), (0, 0) 0 − 0 ≥ −6 4(−6) − (−2) ≥ −6 0 ≥ −6 −24 + 2 ≥ −6 (0, 0) is a solution −22 ≥ −6 (-2, -6) is not a solution Tue, Dec 01
  37. 37. EXAMPLE 1 Tell whether the given coordinates satisfy each inequality by testing each point. Is the bondary line solid or dashed? b. 4y − x ≥ −6 4(0) − 0 ≥ −6 (-2, -6), (0, 0) 0 − 0 ≥ −6 4(−6) − (−2) ≥ −6 0 ≥ −6 −24 + 2 ≥ −6 (0, 0) is a solution −22 ≥ −6 The boundary line is solid (-2, -6) is not a solution Tue, Dec 01
  38. 38. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 Tue, Dec 01
  39. 39. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m=3 Tue, Dec 01
  40. 40. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 Tue, Dec 01
  41. 41. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Tue, Dec 01
  42. 42. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Tue, Dec 01
  43. 43. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Tue, Dec 01
  44. 44. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Tue, Dec 01
  45. 45. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Tue, Dec 01
  46. 46. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Tue, Dec 01
  47. 47. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Tue, Dec 01
  48. 48. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Tue, Dec 01
  49. 49. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Check (0, 0): Tue, Dec 01
  50. 50. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Check (0, 0): 0 > 3(0) − 5 Tue, Dec 01
  51. 51. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Check (0, 0): 0 > 3(0) − 5 Tue, Dec 01
  52. 52. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Check (0, 0): 0 > 3(0) − 5 Tue, Dec 01
  53. 53. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5) Boundary line is dashed Check (0, 0): 0 > 3(0) − 5 Tue, Dec 01
  54. 54. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 Tue, Dec 01
  55. 55. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m=− 2 Tue, Dec 01
  56. 56. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 Tue, Dec 01
  57. 57. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Tue, Dec 01
  58. 58. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid Tue, Dec 01
  59. 59. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid Tue, Dec 01
  60. 60. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid Tue, Dec 01
  61. 61. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid Tue, Dec 01
  62. 62. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid Tue, Dec 01
  63. 63. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid Tue, Dec 01
  64. 64. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid Tue, Dec 01
  65. 65. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid Check (0, 0): Tue, Dec 01
  66. 66. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid 3 Check (0, 0): 0 ≤ − (0) + 4 2 Tue, Dec 01
  67. 67. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid 3 Check (0, 0): 0 ≤ − (0) + 4 2 Tue, Dec 01
  68. 68. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid 3 Check (0, 0): 0 ≤ − (0) + 4 2 Tue, Dec 01
  69. 69. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2 y-int: (0, 4) Boundary line is solid 3 Check (0, 0): 0 ≤ − (0) + 4 2 Tue, Dec 01
  70. 70. WHERE TO SHADE Tue, Dec 01
  71. 71. WHERE TO SHADE When y is isolated, there is a trick we can use: Tue, Dec 01
  72. 72. WHERE TO SHADE When y is isolated, there is a trick we can use: y goes down when we get less (<, ≤), so shade below Tue, Dec 01
  73. 73. WHERE TO SHADE When y is isolated, there is a trick we can use: y goes down when we get less (<, ≤), so shade below y goes up when we get less (>, ≥), so shade above Tue, Dec 01
  74. 74. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. Tue, Dec 01
  75. 75. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. x = length, y = width Tue, Dec 01
  76. 76. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. x = length, y = width P = 2x + 2y Tue, Dec 01
  77. 77. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. x = length, y = width P = 2x + 2y 10 ≤ 2x + 2y Tue, Dec 01
  78. 78. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. x = length, y = width P = 2x + 2y 10 ≤ 2x + 2y -2x -2x Tue, Dec 01
  79. 79. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. x = length, y = width P = 2x + 2y 10 ≤ 2x + 2y -2x -2x 10 − 2x ≤ 2y Tue, Dec 01
  80. 80. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. x = length, y = width P = 2x + 2y 10 ≤ 2x + 2y -2x -2x 10 − 2x ≤ 2y 2 2 Tue, Dec 01
  81. 81. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. x = length, y = width P = 2x + 2y 10 ≤ 2x + 2y -2x -2x 5− x ≤ y 10 − 2x ≤ 2y 2 2 Tue, Dec 01
  82. 82. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation. x = length, y = width P = 2x + 2y 10 ≤ 2x + 2y -2x -2x 5− x ≤ y 10 − 2x ≤ 2y 2 2 y ≥ −x + 5 Tue, Dec 01
  83. 83. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  84. 84. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  85. 85. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  86. 86. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  87. 87. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  88. 88. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  89. 89. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  90. 90. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  91. 91. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  92. 92. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  93. 93. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5 Tue, Dec 01
  94. 94. EXAMPLE 3 c. Does the “trick” tell us to shade above or below the boundary line? How do you know? d. Use the graph to name three possible combinations of length and width for rectangle ABCD. Check to make sure they satisfy the situation. Tue, Dec 01
  95. 95. EXAMPLE 3 c. Does the “trick” tell us to shade above or below the boundary line? How do you know? You shade above, as y gets larger due to ≥ d. Use the graph to name three possible combinations of length and width for rectangle ABCD. Check to make sure they satisfy the situation. Tue, Dec 01
  96. 96. EXAMPLE 3 c. Does the “trick” tell us to shade above or below the boundary line? How do you know? You shade above, as y gets larger due to ≥ d. Use the graph to name three possible combinations of length and width for rectangle ABCD. Check to make sure they satisfy the situation. Any points on the line or the shaded region work. The values must be positive in this situation. Tue, Dec 01
  97. 97. HOMEWORK Tue, Dec 01
  98. 98. HOMEWORK p. 260 #1-37 odd “Everyone has talent. What is rare is the courage to follow the talent to the dark place where it leads.” - Erica Jong Tue, Dec 01

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