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Thread: find x if the slope of the line...

  1. #1
    Super Member bigwave's Avatar
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    Cool find x if the slope of the line...

    find $\displaystyle x$ if the slope of the line through $\displaystyle (1,2)$ and $\displaystyle (x,0)$ is the negative of the slope of the
    line through $\displaystyle (4,5)$ and $\displaystyle (x,0)$
    I know that these slopes do not have to be perpendicular to each other.
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  2. #2
    Super Member General's Avatar
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    Let $\displaystyle m_1$ be the slope of the first line, and $\displaystyle m_2$ be the slope of the second line ..

    Since the slope of the first line is the negative of the slope of the second line, we conclude that :

    $\displaystyle m_1=-m_2$ ..... (1)

    $\displaystyle m_1=\frac{0-2}{x-1}=\frac{-2}{x-1}$ ... (2)

    $\displaystyle m_2=\frac{0-5}{x-4}=\frac{-5}{x-4}$ ... (3)

    If we substitute (2) & (3) in (1), we will get the following equation :

    $\displaystyle \frac{-2}{x-1}=\frac{5}{x-4}$

    Solve the last equation for $\displaystyle x$.
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  3. #3
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    you have to solve:
    -2/(x-1)=5/(x-4)
    if x<>1 and x<>4 then this is equivalent to -2(x-4)=5(x-1)
    7x=13
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