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Math Help - Find Equation of Parallel and Perpendicular Lines

  1. #1
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    Find Equation of Parallel and Perpendicular Lines

    Find an equation of the following parallel and perpendicular lines.

    A.) The line parallel to x+3=0 and passing through (-6, -7)

    B.) The line perpendicular to y-4=0 passing through (-1, 6)

    Is there a specific formula I can use to to solve these?
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by larry21 View Post
    Find an equation of the following parallel and perpendicular lines.

    A.) The line parallel to x+3=0 and passing through (-6, -7)

    B.) The line perpendicular to y-4=0 passing through (-1, 6)

    Is there a specific formula I can use to to solve these?

    The equation of a line passing through a point (x_1, y_1) is given by:

    y-y_1 = m(x-x_1)

    where m is the slope.

    Now, two lines are parallel if their slopes are equal.

    and two lines are perpendicular if the product of their slopes is -1.
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  3. #3
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by harish21 View Post
    y-y_1 = m(x-x_1)
    For reference, this equation is known as the point-slope equation.
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  4. #4
    Senior Member nikhil's Avatar
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    1)required line is parallel to x+3=0 and passes through (-6,-7)
    equation of such line will be x=c. since it passes through (-6,-7)
    -6=c or
    x=-6
    x+6=0
    [NOTE: line x+k=0 is perpendicular to x axis so any line parallel to it must also be perpendicular to x axis and in the form x+k=0]

    2) line perpendicular to y-4=0 will be in the form x=c.
    since it passes through(-1,6)
    we have -1=c
    or c=-1
    x=-1
    x+1=0
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