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Rate-of-ChangeSlope Worksheet

By Doris Andrews,2014-03-31 21:11
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Rate-of-ChangeSlope Worksheet

    Rate-of-Change/Slope Worksheet

    Formulas

    -y or rise or change in y Slope = m = y21

     x-x run change in x 21

1. Graph and label each line by its two points, and compute the slope.

    L1: p=(0,0) p=(5,5) m= (5-0)/(5-0) = 1 12

    L2: p=(1,1) p=(-3,5) m= (5-1)/(-3-1) =-1 12

    L3: p=(-3,-3) p=(6,-3) m= (-3-(-3))/(6-(-3)) = 0 12

    L4: p=(0,-7) p=(7,0) m= (0-(-7))/(7-0) = 1 12

    L5: p=(-8,-3) p=(-8,3) m= (3-(-3))/(-8-(-8)) = 12

     = 6/0 UNDEFINED

Questions:

    ; Which 2 lines are parallel? L1 & L4

    ; What can you say about their slopes? equal

    ; What does a line with slope 0 look like?

    horizontal

    ; What is the slope of a vertical line?

     undefined

    s 2. What is the slope of each of the following lines?

    Be sure to list which points you select as p1 &

    p2.

    L1: p=(-2,7), p=(6,5) m= 5-7 _ = -1 12

     6-(-2) 4

     L2: p=(-7,-9), p=(3,-4) m= -4-(-9) _ = 1 12

     3-(-7) 2

    L3: p=(-4,6), p=(-2,-4) m= -4-6 _ = -10 = -5 12

     -2-(-4) 2

    Questions: What can you say about the “tilt” of

    lines with positive and negative slopes?

    d +slope -> lower left-upper right, -slope -> upper left-lower right

    Which line has greatest slope? L2 Least slope? L3 (steep slope, but negative!)

3. Challenge Question:

    Consider the following data

    from USA Today on the

    number of students applying

    to colleges using the “early

    admission” option.

    Make a scatter plot of the 7

    points, draw a straight line

    that seems to be a best fit,

    determine the slope of this

    line, and make a prediction

    for 2005-6.

m=94,000-54,000 = 40000

    2005-1999 6

     = 6666 students/year

2005 ? 94,000 students

     d 100,000

    90,000

    80,000

    70,000

    60,000

    50,000

    40,000

    d 1997 1998 1999 2000 2001 2002 2003 2004 2005

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