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Math Help - Find the equation of a line that is perpendicular to another.

  1. #1
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    Find the equation of a line that is perpendicular to another.

    Okay, so I am given that the the equation passes through the point (-4, 2) and is perpendicular to 10x - 2y - 6 = 0. Dolefully I have done the calculations, over and over, producing the same results. I put the equation into slope-intercept and procure y = 5x -3
    So, m_1 = 5 and m_2 = -1/5. I then take the new slope and use the point-slope equation and, after all of the calculations, find myself with the resultant: 5x + y + 18 = 0
    (they ask it to be formatted into general form). The true answer, according the answer key, is x + 5y - 6 = 0--this can not be true!
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    MHF Contributor Siron's Avatar
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    Re: Find the equation of a line that is perpendicular to another.

    The slope of the line which you're searching is indeed \frac{-1}{5} that means we have untill now the equation: y=\frac{-1}{5}x+q
    We have to find q this can be done by substituting the given point into the equation:
    2=\frac{4}{5}+q \Leftrightarrow q=2-\frac{4}{5} \Leftrightarrow q=\frac{6}{5}
    Therefore the equation of the straight line becomes:
    y=\frac{-1}{5}x+\frac{6}{5}
    \Leftrightarrow 5y=-x+6
    \Leftrightarrow 5y+x-6=0
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    Re: Find the equation of a line that is perpendicular to another.

    Why wouldn't the point-slope formula work?
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    Re: Find the equation of a line that is perpendicular to another.

    y = -x/5 + b ; substitute -4,2:
    b = 6/5

    y = -x/5 + 6/5
    Take over...
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    MHF Contributor Siron's Avatar
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    Re: Find the equation of a line that is perpendicular to another.

    If you mean:
    y-2=\frac{-1}{5}\left(x+4)
    \Leftrightarrow y-2=\frac{-x}{5}-\frac{4}{5}
    \Leftrightarrow 5y-10=-x-4
    \Leftrightarrow 5y+x-10+4=0
    \Leftrightarrow 5y+x-6=0
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    Re: Find the equation of a line that is perpendicular to another.

    Well, what formula is this then:

    m= (x - x_1)/(y - Y_1)?
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    Re: Find the equation of a line that is perpendicular to another.

    Quote Originally Posted by Bashyboy View Post
    Why wouldn't the point-slope formula work?
    It will...go study:
    Straight-Line Equations: Point-Slope Form
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