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Math Help - lines in xy

  1. #1
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    lines in xy

    I can't believe I'm having so much trouble

    #1:

    For which values of k are the following pairs of lines parallel? perpendicular?
    3x+4y=9
    x+ky=6



    #2:

    (k-1)y+(k+1)x+k-1=0 (k is a constant)
    For what value of k is the graph of this function parallel to the x-axis?

    I tried re-arranging it, but it confused me even more.

    Please help
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  2. #2
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    Quote Originally Posted by starship View Post
    I can't believe I'm having so much trouble

    #1:

    For which values of k are the following pairs of lines parallel? perpendicular?
    3x+4y=9
    x+ky=6

    ...
    Two lines l_1 and l_2 are parallel if their slopes are equal.

    Two lines l_1 and l_2 are perpendicular if the product of their slopes equals (-1).

    l_1: 3x+4y = 9~\implies~y = -\frac34 x + \frac94

    l_2: x+ ky = 6~\implies~ y = -\frac1k x + \frac6k

    l_1 \parallel l_2: -\frac34 = -\frac1k Solve for k

    l_1 \bot l_2: \left(-\frac34\right) \cdot \left(-\frac1k\right) = -1 . Solve for k
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  3. #3
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    Quote Originally Posted by starship View Post
    ...
    #2:

    (k-1)y+(k+1)x+k-1=0 (k is a constant)
    For what value of k is the graph of this function parallel to the x-axis?

    ...
    A line with the equation y = a~,~a  \in \mathbb{R} is a parallel to the x-axis that means the coefficient of x must be zero:

    (k-1)y+(k+1)x+k-1=0 that means: k+1=0~\iff~ k = -1
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