What is the equation of the line perpendicular to #y=-1/5x # that passes through # (7,4) #?

1 Answer
Dec 23, 2015

Answer:

#5x-y=31#

Explanation:

#y=-1/5x# has a slope of #(-1/5)#
all line perpendicular to this will have a slope of #5#
(if a line has a slope of #m#, lines perpendicular to it have a slope of #(-1/m)#)

If a line has a slope #m=5# and passes through the point #(barx,bary)=(7,4)#
then we can write the equation of this line in "slope-point" form as
#color(white)("XXX")(y-bary)=m(x-barx)#

In this case
#color(white)("XXX")(y-4)=5(x-7)#

While this is a valid answer to the given question, let's convert it into standard form: #ax+by=c# with #a,b,c in ZZ; a>=0#

#color(white)("XXX")y-4=5x-35#

#color(white)("XXX")5x-y=31#