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Math Help - Find the intersections of the lines

  1. #1
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    Find the intersections of the lines

    l : 3x+4y =5 and m: (x,y) = (2, -4) + t(2,6)

    So, I was thinking i could turn m into slope form, like l is..

    so I think m: (x,y) = (2, -4) + t(2,6) is also y = 3x - 10

    and then I just find where they are equal? or use system of linear equations and substitute?
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  2. #2
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    Quote Originally Posted by zodiacbrave View Post
    l : 3x+4y =5 and m: (x,y) = (2, -4) + t(2,6)

    So, I was thinking i could turn m into slope form, like l is..

    so I think m: (x,y) = (2, -4) + t(2,6) is also y = 3x - 10

    and then I just find where they are equal? or use system of linear equations and substitute?
    Use your parametric form in the general form. i.e. if x = 2 + 2t and y = -4 + 6t then

    3(2 + 2t ) + 4(-4 + 6t) = 5 and solve for t. Once you have this, sub. back into your parametric form.

    Spoiler:
    t = \frac{1}{2} and the point is (3,-1)
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