SECTION 6-4
Write and Graph Linear Inequalities
ESSENTIAL QUESTIONS

How do you write linear inequalities in two variables?

How do you graph linear inequalities in two v...
VOCABULARY

1. Open Half-plane:

2. Boundary:
3. Linear Inequality:

4. Solution to the Inequality:
VOCABULARY

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

4. Solut...
VOCABULARY

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

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

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

5. Graph of the Inequality:



6. Closed Half-plane:

7.Test Point:
VOCABULARY

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

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

5. Graph of the Inequality: Includes graphing the
    boundary line and the shaded half-plane that
    include...
GRAPHING A LINEAR
   INEQUALITY
GRAPHING A LINEAR
         INEQUALITY
Begin by treating the inequality as an equation to
graph the boundary line and isola...
GRAPHING A LINEAR
         INEQUALITY
Begin by treating the inequality as an equation to
graph the boundary line and isola...
GRAPHING A LINEAR
         INEQUALITY
Begin by treating the inequality as an equation to
graph the boundary line and isola...
GRAPHING A LINEAR
         INEQUALITY
Begin by treating the inequality as an equation to
graph the boundary line and isola...
GRAPHING A LINEAR
         INEQUALITY
Begin by treating the inequality as an equation to
graph the boundary line and isola...
EXAMPLE 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    Graph the following inequalities.
a. y > 3x − 5
EXAMPLE 2

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

m=3
EXAMPLE 2

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

m = 3 Up 3, right 1
EXAMPLE 2

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

m = 3 Up 3, right 1

   y-int: (0, -5)
EXAMPLE 2

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

  m = 3 Up 3, right 1

      y-int: (0, -5)

Bo...
EXAMPLE 2

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

  m = 3 Up 3, right 1

      y-int: (0, -5)

Bo...
EXAMPLE 2

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

  m = 3 Up 3, right 1

      y-int: (0, -5)

Bo...
EXAMPLE 2

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

  m = 3 Up 3, right 1

      y-int: (0, -5)

Bo...
EXAMPLE 2

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

  m = 3 Up 3, right 1

      y-int: (0, -5)

Bo...
EXAMPLE 2

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

  m = 3 Up 3, right 1

      y-int: (0, -5)

Bo...
EXAMPLE 2

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

  m = 3 Up 3, right 1

      y-int: (0, -5)

Bo...
EXAMPLE 2

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

   m = 3 Up 3, right 1

      y-int: (0, -5)

...
EXAMPLE 2

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

   m = 3 Up 3, right 1

       y-int: (0, -5)...
EXAMPLE 2

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

   m = 3 Up 3, right 1

       y-int: (0, -5)...
EXAMPLE 2

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

   m = 3 Up 3, right 1

       y-int: (0, -5)...
EXAMPLE 2

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

   m = 3 Up 3, right 1

       y-int: (0, -5)...
EXAMPLE 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

           Graph the following inequalities.
               3
    b. y ≤ − x + 4
               2
       3
m = ...
WHERE TO SHADE
WHERE TO SHADE


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


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

y goes down when we get less (<, ≤), so shade below
WHERE TO SHADE


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

y goes down when we get less (<, ≤), so shade below
...
EXAMPLE 3

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

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

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

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

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

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

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

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

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

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

b. Graph the solution to the inequality.
              y ≥ −x + 5
EXAMPLE 3

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



d. Use the...
EXAMPLE 3

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

      You sh...
EXAMPLE 3

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

      You sh...
HOMEWORK
HOMEWORK



               p. 260 #1-37 odd




“Everyone has talent. What is rare is the courage
 to follow the talent to...
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Integrated 2 Section 6-4

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  • Integrated 2 Section 6-4

    1. 1. SECTION 6-4 Write and Graph Linear Inequalities
    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
    3. 3. VOCABULARY 1. Open Half-plane: 2. Boundary: 3. Linear Inequality: 4. Solution to the Inequality:
    4. 4. VOCABULARY 1. Open Half-plane: A dashed boundary line separates the plane 2. Boundary: 3. Linear Inequality: 4. Solution to the Inequality:
    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:
    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:
    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
    8. 8. VOCABULARY 5. Graph of the Inequality: 6. Closed Half-plane: 7.Test Point:
    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:
    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:
    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
    12. 12. GRAPHING A LINEAR INEQUALITY
    13. 13. GRAPHING A LINEAR INEQUALITY Begin by treating the inequality as an equation to graph the boundary line and isolate y.
    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.
    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.
    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
    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
    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)
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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)
    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
    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
    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
    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
    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
    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
    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
    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
    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
    38. 38. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5
    39. 39. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m=3
    40. 40. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1
    41. 41. EXAMPLE 2 Graph the following inequalities. a. y > 3x − 5 m = 3 Up 3, right 1 y-int: (0, -5)
    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
    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
    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
    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
    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
    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
    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
    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):
    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
    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
    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
    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
    54. 54. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2
    55. 55. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m=− 2
    56. 56. EXAMPLE 2 Graph the following inequalities. 3 b. y ≤ − x + 4 2 3 m = − Down 3, right 2 2
    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)
    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
    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
    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
    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
    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
    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
    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
    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):
    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
    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
    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
    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
    70. 70. WHERE TO SHADE
    71. 71. WHERE TO SHADE When y is isolated, there is a trick we can use:
    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
    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
    74. 74. EXAMPLE 3 Rectangle ABCD has a perimeter of at least 10 cm. a. Write a linear inequality that represents the situation.
    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
    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
    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
    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
    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
    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
    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
    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
    83. 83. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    84. 84. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    85. 85. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    86. 86. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    87. 87. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    88. 88. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    89. 89. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    90. 90. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    91. 91. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    92. 92. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    93. 93. EXAMPLE 3 b. Graph the solution to the inequality. y ≥ −x + 5
    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.
    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.
    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.
    97. 97. HOMEWORK
    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

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