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Thread: Find values of k if Parallel or if Perpendicular

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    Find values of k if Parallel or if Perpendicular

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

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

    $\displaystyle {k^2}=16$

    $\displaystyle
    k=\sqrt{16}=4
    $

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

    B.) Are there any values of $\displaystyle k$ 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 $\displaystyle k$ for which the lines $\displaystyle kx-2y-1=0$ and $\displaystyle 8x-ky+3=0$ are parallel.

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

    $\displaystyle {k^2}=16$

    $\displaystyle
    k=\sqrt{16}=4
    $

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

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

    How would I be able to find out?
    A)

    The following is true

    $\displaystyle x=4 \Longrightarrow x^2 = 16$

    The following is not true

    $\displaystyle x^2 = 16 \Longrightarrow x = 4$

    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

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

    You will get k = 0.
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