What is the equation of the line passing through #(5,8)# and #(12,3)#?

1 Answer
Alan P.
Dec 23, 2015

#5x+7y=81#

Explanation:

The slope between #(5,8)# and #(12,3)# is
#color(white)("XXX")m=(3-8)/(12-5)= -5/7#

Using this slope and one of the points (I picked #(5,8)# but either would work)
we can apply the slope-point form: #(y-bary)=m(x-barx)# to get
#color(white)("XXX")y-8 = (-5/7)(x-5)#
which is a perfectly valid answer to the given question.

However, let's continue and convert it into standard form: #ax+by=c#

#color(white)("XXX")7(y-8)=-5(x-5)#

#color(white)("XXX")7y-56=-5x+25#

#color(white)("XXX")5x+7y=81#

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