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2 Different answers given the same point and slope

  1. Sep 16, 2007 #1
    1. The problem statement, all variables and given/known data
    Given the point (1,9) on a curve, and the slope = 4, what is the equation of the tangent line to the point?

    2. Relevant equations
    #1) y-y1 = m (x-x1)
    #2) y = mx+b

    3. The attempt at a solution
    Using equation #1, I got y = 4x-3
    Using equation #2, I got y = 4x+5

    What am I doing wrong here?
  2. jcsd
  3. Sep 16, 2007 #2


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    How did you get each of the answers in section 3 of your post?
  4. Sep 16, 2007 #3
    Here are my computations:

    1) y-y1 = m(x-x1):
    y-1 = 4 (x-1)
    y = 4x - 4 + 1
    y = 4x -3

    2) y = mx +b
    9 = 4 (1) + b
    5 = b
    therefore, y = 4x + 5
  5. Sep 16, 2007 #4


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    In this point-slope equation, isn't y1 = 9?
  6. Sep 16, 2007 #5
    Yes, you're right! I really made a silly mistake. Thank you!
  7. Sep 16, 2007 #6


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    From my long years of having taken exams, graded exams, and helped students with post-mortems on exams, I can tell you that the number 1 type of mistake people make is *sign* errors and the number 2 type is *copying* errors. Everyone, including the professionals, makes them (occasionally, these errors even get into published journal papers!). Knowing this won't keep you from ever making mistakes again, but it does help you keep alert for where things may have gone wrong...
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