How do you write the equation of the line in the form AX+BY=C if (2,5) ; m=3/1?

1 Answer
Sep 16, 2015

#3x-1y=1

Explanation:

Given the point #(2,5)# and the slope #m=3/1#
we can start with the slope-point form for the line:
#color(white)("XXX")(y-haty) = m(x-hatx)#
or, for the given values:
#color(white)("XXX")(y-5) = 3(x-2)#

Simplifying
#color(white)("XXX")y-5 = 3x-6#

Rearranging so variables are on the left and constant is on the right:
#color(white)("XXX")-3x + y = -1#

There is normally a requirement that #A# of #Ax+By=C# be #>=0#
In this case:
#color(white)("XXX")3x-1y=1#