Algebra I

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Stephen is walking from his house to his friend Sharon's house. When he is 12 blocks away, he looks at his watch. He looks again when he is 8 blocks away and finds that 6 minutes have passed. Write 2 ordered pairs for these data in the form (time, blocks).
Write a linear equation for these 2 points.
What is the total amount of time it takes Stephen to reach Sharon's house? Explain please.

  • Algebra I -

    (time t, blocks d)
    (0 , 12)
    (6 , 8 )
    d is distance from house in blocks
    d = m t + b
    12 = 0 + b so b = 12
    8 = m *6 + 12
    -4/6 = m
    m = -2/3
    so
    d = -(2/3) t + 12
    0 = -(2/3) t + 12
    t = (3/2) * 12 = 18 minutes

  • Algebra I -

    the two ordered pairs from your information are
    (0,12) and (6,8)

    slope = (12-8)/-6
    = -2/3

    So Blocks = (-2/3)t + b
    using (0,12)
    12 = 0 = b
    b = 12
    so the linear equation is

    Blocks = (-2/3)Time + 12

    when he reaches Sharon's house Blocks = 0
    so 0 = (-2/3)time + 12
    (2/3)time = 12
    time = 18

    it will take 18 minutes

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