What is the equation of the line perpendicular to #y=-5/11x # that passes through # (1,-3) #?

1 Answer
Alan P.
Dec 7, 2015

#11x-5y=26#

Explanation:

#y=-5/11x# has a slope of #(-5/11)#

For any line with a slope of #m# all lines perpendicular to it have a slope of #(-1/m)#

Therefore any line perpendicular to #y=-5/11x# has a slope of #11/5#.

If such a line passes through the point #(1,-3)# then we can write its equation in the slope-point form (#y-haty=m(x-hatx)#)

So our required line can be written as:
#color(white)("XXX")y-(-3) = 11/5(x-1)#

While this is a valid answer to the given question, we would normally simplify it and convert it into standard form:

#color(white)("XXX")5(y+3)=11(x-1)#

#color(white)("XXX")5y+15 = 11x -11#

#color(white)("XXX")26 = 11x -5y#

#color(white)("XXX")11x -5y = 26#

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