How do you write the equation of the line in the form AX+BY=C if (9, -8) and (0, 3)?

1 Answer
Pythagoras
Sep 20, 2015

#11/9 x +y=3#

Explanation:

Okay, the line passes through these two points, and the equation of a line is usually in the form #y=ax+b#.

Then the point (9, -8) is because:
#-8=a*9+b#
and the point (0, 3) is because:
#3=a*0+b#

We just need to solve for a and b to find the equation of the line.
From the second equation we readily see that #b=3#.

Now substitute this #b# into the equation of the first point:
#-8=a*9+3#
Rearranging, we have:
#9a=-11#
so #a=-11/9#

So the equation of the line is: #y=-11/9 x +3#
Rearranging, we get:
#11/9 x +y=3#
which is in the desired form #Ax+By=C#
where #A=11/9#, #B=1#, and #C=3#

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