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Math Help - Cartesan equation to parametric and vector form

  1. #1
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    Cartesan equation to parametric and vector form

    Please check and please explain if it is incorrect, even if it is correct. have a very vague understanding of it. Thank you.

    Convert the following Cartesan equation to parametric and vector form
    3x-5y=9
    y=-9/5+3/5x
    y=-6/5 + 3/5(x-1)
    y=-6/5+3/5t
    t=x-1

    x=t+1
    y=-6/5+3/5t
    How to write it in a vector form?
    Thank you
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  2. #2
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    Here is one way.
    The the points (3,0)~\&~(-2,-3) are on the line. (You can pick any two.)
    Therefore, the vector they determine, <5,3>, directs the line.
    So the parametric form is \begin{gathered}<br />
  x = 5t + 3 \hfill \\<br />
  y = 3t \hfill \\ <br />
\end{gathered}
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  3. #3
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    Plato,

    thank you and I have questions. Why vector is <5,3>, and not <-5, -3>
    If we select two points (3,0) and (-2,-3), then v=<-2-3, -3-0>=<-5,-3>
    the vector form is -5i-3j
    I know it is wrong because your answer is different, but why?
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  4. #4
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    Quote Originally Posted by oceanmd View Post
    Why vector is <5,3>, and not <-5, -3>
    Don't you understand that both <5,3>~\&~<-5,-3> are the same direction of that line?
    They are negatives of each other, therefore parallel.
    The vectors <15,9>~\&~<-10,-6> are also direction vectors of that line.
    Any vector parallel to <5,3> is a direction vector of the line.
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  5. #5
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    parametric form question

    Plato,
    got you. Thanks.
    As for the parametric form, is it a rule that if a vector is let say <7,5>, then parametric form is x=7t+5 and y=5t ?

    Thank you
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