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Math Help - Perpendicular Lines

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    Member Rimas's Avatar
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    Perpendicular Lines

    Find all a for which the lines represented by the equations 2y+3+x=0 and 3y+ax+2=0 are perpendicular
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Rimas View Post
    Find all a for which the lines represented by the equations 2y+3+x=0 and 3y+ax+2=0 are perpendicular
    Put the first line equation in slope-intercept form:
    2y + 3 + x = 0

    y = -(1/2)x - (3/2)

    The second line needs to have a slope of +2 to be perpendicular to this line.

    Thus:
    3y + ax + 2 = 0

    y = -(a/3)x - (2/3)

    Thus -a/3 = 2. Thus a = -6.

    -Dan
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    Quote Originally Posted by Rimas View Post
    Find all a for which the lines represented by the equations 2y+3+x=0 and 3y+ax+2=0 are perpendicular
    If line l_1 has slope m_1 and line l_2 has slope m_2 then if neither line is vertical then the two line are perpendicular if (m_1)(m_2)=-1.
    2y+3+x=0 has slope (-1/2); 3y+ax+2=0 has slope (-a/3).
    Now solve for a.
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