Question 534332
(1)
(-1,-4)
{{{ y = (1/6)*x + 1 }}}
This is in the form {{{ y = m*x + b }}}, where {{{ m }}} = slope
ANY line perpendicular to this line
will have slope = {{{ - 1/m }}} 
Your equation has {{{ m = 1/6 }}}, so any line
perpendicular to it has slope = {{{ - (1/(1/6)) = -6 }}}
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So far you have {{{ y = -6x + b }}}. To find {{{b}}}, plug in
(x,y) = (-1,-4)
{{{ -4 = -6*(-1) + b }}}
{{{ -4 = 6 + b }}}
{{{ b = -4 - 6 }}}
{{{ b = -10 }}}
The equation of the perpendicular line is {{{ y = -6x - 10 }}}
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(2)
(-5,5)
{{{ y = -5x + 9 }}}
Slope of any perpendicular line = {{{ -(1/(-5)) = 1/5 }}}
Now plug in (x,y) = (-5,5)
{{{ 5 = (1/5)*(-5) + b }}}
{{{ 5 = -1 + b }}}
{{{ b = 6 }}}
The equation is {{{ y = (1/5)*x + 6 }}}
Here's a plot of these 2 lines:
{{{ graph( 400, 400, -12, 12, -12, 12, -5x + 9, (1/5)*x + 6) }}}