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Simple question: Find equation of a line thru 2 points. Thanks.

  1. Aug 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Just doing some review, and I keep getting the wrong answer. Can someone explain this for me please?

    The equation of the straight line through the points (-€2; 1) and (2; 3) is

    Book says the correct answer is 2y = x + 4

    What are the steps to get 2y = x + 4 ???

    2. Relevant equations



    3. The attempt at a solution

    Here is what I did:

    Slope = 1/2
    so y =1/2x + c

    taking 2 points, 2,3 as in x and y

    3=1/2(2)+c
    3=1/4+c

    2.75=c

    so y=1/2x + 2.75

    Im so lost....:(
     
  2. jcsd
  3. Aug 21, 2012 #2

    Mark44

    Staff: Mentor

    (1/2)(2) = 1, not 1/4.
     
  4. Aug 21, 2012 #3
    Ahhhg, why did I put that! lol

    Right, so:

    I still dont quite udnerstand how the book got 2y = x + 4
     
  5. Aug 21, 2012 #4
    Ok here is what I got for finding an equation of a line thru these points: (-2,1) (2,3)

    m = 1/2

    so taking the points 2,3 I get the following:

    3 = 1/2(2) + c

    3 = 1 + c

    2 = c

    so, y = 1/2x + 2

    But thats wrong...?
     
  6. Aug 21, 2012 #5

    SammyS

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    It's clearer if you write it as
    y = (1/2)x + 2 .​
    That line does pass through points: (-2,1) and (2,3) .
     
  7. Aug 21, 2012 #6
    Then why does my book say this is the correct answer? 2y = x + 4

    Is it because the book did not like the 1/2, so it multiplied it by 2 to get 1, and did same to all sides?
     
  8. Aug 21, 2012 #7

    SammyS

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    Yes .
     
  9. Aug 23, 2012 #8
    2y = x + 4 and y = 1/2 + 2 are the exact same things. The first way is just a little easier to write.

    Easiest way to go about these problems for me is a system of equations.

    y = mx + b
    plug in conditions:
    (1) 1 = -2x + b
    (2) 3 = 2m + b

    By adding (1) and (2), we obtain 4 = 2b, so b = 2

    Plug b = 2 into (2) (we could have picked either equation), we get 1 = 2m, so m = 1/2

    plugging back in to the original formula, we get y = (1/2)x + 2, or 2y = x + 4, both are correct.
     
  10. Aug 23, 2012 #9

    Mark44

    Staff: Mentor

    No, 2y = x + 4 and y = (1/2)x+ 2 are the same. (Technically, they are equivalent equations.)
     
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