How do you write the equation of the line in the form AX+BY=C if A(6, -1) and B (-3, 7)?

1 Answer
Sasha P.
Sep 13, 2015

8x+9y=39

Explanation:

Let's start with equation of the line in the form #y=kx+n#. We have two points with #x# and #y# coordinates, e.g. for point A: #x=6, y=-1#, for point B: #x=-3, y-7#. Next, we insert those coordinates in the equation mentioned above and get 2 equation:
for A: #-1=6k+n#
for B: #7=-3k+n#
Now, we have to solve this system of equations, the easiest way is to subtract them. We get:
#-1-7=6k+n-(-3k+n)#
#-8=6k+n+3k-n#
#-8=9k#
#k=-8/9#
#-1=6(-8/9)+n#
#n=-1+48/9#
#n=39/9#
So, finding #k, n# we can form #y=kx+n#
#y=-8/9x+39/9#
Multiplying whole equation with 9:
#9y=-8x+39#
we finally get:
#8x+9y=39#

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