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Math Help - Find values of k if Parallel or if Perpendicular

  1. #1
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    Find values of k if Parallel or if Perpendicular

    Find the values of k for which the lines kx-2y-1=0 and 8x-ky+3=0 are parallel.

    \frac{k}{2}=\frac{8}{k}

    {k^2}=16

     <br />
k=\sqrt{16}=4<br />

    But my textbook says it's plus or minus 4, I only got +4 why?

    B.) Are there any values of k that would make the two lines perpendicular? Explain.

    How would I be able to find out?
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    Quote Originally Posted by larry21 View Post
    Find the values of k for which the lines kx-2y-1=0 and 8x-ky+3=0 are parallel.

    \frac{k}{2}=\frac{8}{k}

    {k^2}=16

     <br />
k=\sqrt{16}=4<br />

    But my textbook says it's plus or minus 4, I only got +4 why?

    B.) Are there any values of k that would make the two lines perpendicular? Explain.

    How would I be able to find out?
    A)

    The following is true

    x=4 \Longrightarrow x^2 = 16

    The following is not true

    x^2 = 16 \Longrightarrow x = 4

    That's because (-4)(-4) = 16.

    B)

    For perpendicular lines, either

    1) one line is horizontal and the other is vertical, or

    2) the slopes are negative reciprocals of each other.

    So here we set

    \frac{k}{2}=-\frac{k}{8}

    You will get k = 0.
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