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Math Help - Lines in a Plane 9

  1. #1
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    Lines in a Plane 9

    For each of the following lines, state a direction vector with integer components. If possible, name a point on the line with integer coordinates.

    a) x=1/3 + 2t
    y=3 - 2t/3

    so this is my attempt, but I am not sure what I did wrong and how to get the correct answer.

    d=(2, -2/3)
    P=(1/3, 3)

    But now to find integer values of the above..
    d=(3,-1)
    P=(1,9)

    But in the back of the book, the answer is
    d=(3,-1) << which I have, BUT they do not have a possible point on the line.. does it mean that there are no other integer values on the line, or is there answer wrong?
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    a) x=1/3 + 2t
    y=3 - 2t/3
    d=(2, -2/3)
    P=(1/3, 3)

    But now to find integer values of the above..
    d=(3,-1)
    But in the back of the book, the answer is
    d=(3,-1) << which I have, BUT they do not have a possible point on the line.. does it mean that there are no other integer values on the line?
    If we write the equation is this form, 3x+9y=28, then when will a multiple if three be 28?
    Ever?
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