math

parallel and perpendicular lines

Determine an equation of each of the following lines .
*the line perpendicular to y-4=0 and passing through the point (-1,6)

** the line perpendicular to 3x-12y+16=0 and having the same y-intercept as the line 14x-13y-52=0

and explain ....

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  1. Put y-4 = o into the form
    y = m x + b
    y = 0 x + 4
    now the slope of the line perpendicular to that is -1/m = -1/0 which is undefined so we will have to use our heads.
    y = 4 is a horizontal line through y = 4, x = anything.
    x = constant, any constant, is perpendicular to y = 4
    So we want the vertical line x = -1
    That line, x = -1 , passes through all values of y including 6
    ---------------------------------------
    Now
    3x -12 y + 16 = 0
    12 y = 3 x + 16
    y = (1/4)x + 4/3
    what is slope of perpendicular?
    m' = -1/(1/4) = -4
    so the line we want is
    y = -4 x + b
    what is b?
    well when x = 0, -13 y = 52
    y = -52/13
    so
    -52/13 = -4(0) + b
    b = -52/13
    so
    y = -4x -52/13

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  2. Y=-1/4x+8

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