finding the slope using formula by KWo6W5

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									 7-7 Finding Slope of a Line

       Preview


                   Warm Up
                   California Standards
                   Lesson Presentation




Holt CA Course 1
 7-7 Finding Slope of a Line


    Warm Up
    Evaluate each equation for x = –1, 0,
    and 1.

    1. y = 3x       –3, 0, 3
    2. y = x – 7    –8, –7, –6
    3. y = 2x + 5   3, 5, 7
    4. y = 6x – 2   –8, –2, 4



Holt CA Course 1
 7-7 Finding Slope of a Line

                   California
                   Standards
             AF3.4 Plot the values of quantities
       whose ratios are always the same (e.g.
       cost to the number of an item, feet to
       inches, circumference to diameter of a
       circle). Fit a line to the plot and
       understand that the slope of the line equals
       the quantities.
       Also covered:            AF3.3.

Holt CA Course 1
 7-7 Finding Slope of a Line


        Recall that lines have constant slope. For
        a line on the coordinate plane, slope is
        the following ratio:


         vertical change    change in y
                          =
        horizontal change   change in x




Holt CA Course 1
 7-7 Finding Slope of a Line

     If you know any two points on a line, you
     can find the slope of the line without
     graphing. The slope of a line through the
     points (x1, y1) and (x2, y2) is as follows:

                           y2 – y1
                   slope =
                           x 2 – x1

     When finding slope using the ratio above, it does
     not matter which point you choose for (x1, y1)
     and which point you choose for (x2, y2).


Holt CA Course 1
 7-7 Finding Slope of a Line
     Additional Example 1: Finding Slope, Given Two
                         Points
    Find the slope of the line that passes through
    A. (–2, –3) and (4, 6).
     Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).

    y2 – y1 6 – (–3)     Substitute 6 for y2, –3 for y1,
    x2 – x1 = 4 – (–2)   4 for x2, and –2 for x1.
      = 6 + 2 =9
              3
         4+        6
                =3       Simplify.
                   2
     The slope of the line that passes through
     (–2, –3) and (4, 6) is 3.
                            2

Holt CA Course 1
 7-7 Finding Slope of a Line
     Additional Example 1: Finding Slope, Given Two
                         Points
    Find the slope of the line that passes through
    B. (1, 3) and (2, 1).
     Let (x1, y1) be (1, 3) and (x2, y2) be (2, 1).

    y2 – y1 1 – 3         Substitute 1 for y2, 3 for y1,
    x2 – x1 = 2 – 1       2 for x2, and 1 for x1.
              -2          Simplify.
            = 1 = –2

    The slope of the line that passes through
    (1, 3) and (2, 1) is –2.



Holt CA Course 1
 7-7 Finding Slope of a Line
    Additional Example 1: Finding Slope, Given Two
                         Points
    Find the slope of the line that passes through
    C. (3, –2) and (1, –2).
    Let (x1, y1) be (3, –2) and (x2, y2) be (1, –2).
    y2 – y1 –2 – (–2) Substitute -2 for y2, -2 for y1,
    x2 – x1 = 1 – 3   1 for x2, and 3 for x1.
              -2 + 2     Rewrite subtraction as addition of
               =1–3      the opposite.
               0
            = –2 = 0
    The slope of the line that passes through
    (3, –2) and (1, –2) is 0.


Holt CA Course 1
 7-7 Finding Slope of a Line
                   Check It Out! Example 1

    Find the slope of the line that passes through
    A. (–4, –6) and (2, 3).
     Let (x1, y1) be (–4, –6) and (x2, y2) be (2, 3).

         y2 – y1 3 – (–6)     Substitute 3 for y2, –6 for y1,
         x2 – x1 = 2 – (–4)   2 for x2, and –4 for x1.
                 =9 =3
                   6    2
    The slope of the line that passes through
    (–4, –6) and (2, 3) is 3.
                           2



Holt CA Course 1
 7-7 Finding Slope of a Line
                   Check It Out! Example 1
    Find the slope of the line that passes through
    B. (2, 4) and (3, 1).
     Let (x1, y1) be (2, 4) and (x2, y2) be (3, 1).

         y2 – y1 1 – 4         Substitute 1 for y2, 4 for y1,
         x2 – x1 = 3 – 2       3 for x2, and 2 for x1.
                   -3          Simplify.
                 = 1 = –3

    The slope of the line that passes through
    (2, 4) and (3, 1) is –3.



Holt CA Course 1
 7-7 Finding Slope of a Line
                   Check It Out! Example 1
    Find the slope of the line that passes through
    C. (3, –2) and (1, –4).
    Let (x1, y1) be (3, –2) and (x2, y2) be (1, –4).
         y2 – y1 –4 – (–2) Substitute -4 for y2, -2 for y1,
         x2 – x1 = 1 – 3   1 for x2, and 3 for x1.

              = –4 + 3
                   1–
                        2

              = –2 = 1      Simplify.
                 –2
    The slope of the line that passes through
    (3, –2) and (1, –4) is –2.


Holt CA Course 1
 7-7 Finding Slope of a Line
          Additional Example 2: Money Application
  The table shows the total cost of fruit per pound
  purchased at the grocery store. Use the data to
  make a graph. Find the slope of the line and
  explain what it shows.       Cost of Fruit
      Graph the data.




                             Cost


                                    Pounds

Holt CA Course 1
 7-7 Finding Slope of a Line




        Helpful Hint
        You can use any two points to find the
        slope of the line.




Holt CA Course 1
 7-7 Finding Slope of a Line
                   Additional Example 2 Continued

                                            Cost of Fruit
      Find the slope of the line:
         y2 – y1
         x2 – x1




                                     Cost
        30 - 15        Substitute.
        10 - 5

          15 = 3       Multiply.
           5
                                             Pounds
   The slope of the line is 3. This means that for every
   pound of fruit, you will pay another $3.

Holt CA Course 1
 7-7 Finding Slope of a Line
                Check It Out! Example 2
  The table shows the total cost of gas per gallon.
  Use the data to make a graph. Find the slope of
  the line and explain what it shows.
                                 Cost of Gas
        Graph the data.          y

              Cost of Gas          12


           Gallons   Cost

                            Cost
                                    9

              0        0            6

              3        6
                                    3
              6       12
                                   0    3   6   9   x
                                        Gallons

Holt CA Course 1
 7-7 Finding Slope of a Line
               Check It Out! Example 2 Continued
                                               Cost of Gas
      Find the slope of the line:              y

          y2 – y1                         12

          x2 – x1 =




                                   Cost
                                           9
          12 - 6       Substitute.
           6-3                             6


           6       = 2 Multiply.           3
           3
                                          0        3   6   9   x
                                                   Gallons
    The slope of the line is 2. This means that for every
    gallon of gas, you will pay another $2.

Holt CA Course 1
 7-7 Finding Slope of a Line




        The slope of a line may be positive, negative,
        zero, or undefined. You can tell which of these
        is the case by looking at the graphs of a line—
        you do not need to calculate the slope.




Holt CA Course 1
 7-7 Finding Slope of a Line




Holt CA Course 1
 7-7 Finding Slope of a Line




Holt CA Course 1
 7-7 Finding Slope of a Line
                    Lesson Quiz: Part I

     Find the slope of the line that passes
     through each pair of points.
     1. (4, 3) and (–1, 1)    2
                              5


     2. (–1, 5) and (4, 2)   –3
                              5




Holt CA Course 1
 7-7 Finding Slope of a Line
                     Lesson Quiz: Part II
     3. The table shows how much money Susan earned
        as a house painter for one afternoon. Use the
        data to make a graph. Find the slope of the line
        and explain what it shows. y
     The slope of the line is 7.
     This means Susan earned       80
     $7 for each hour worked.      70
                                   60
                                   50
                                   40
                                   30
                                   20
                                   10
                                                             x
                                   0    2   4 6 8 10 12 14




Holt CA Course 1

								
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