A line passes through the points (-3,-5) and (6,7). The equation of this line can be expressed in the form Ax + By = C, where A, B, and C are integers with greatest common divisor 1, and A is positive. Find A + B+ C.
Slope = ( 7 - -5) / ( 6 - -3) = 12/9 = 4/3
Using either point we can write the equation as
y = (4/3) (x - 6) + 7 multiply through by 3
3y = 4(x - 6) + 21
3y = 4x - 24 + 21
3y = 4x - 3 rearrange as
4x - 3y = 3
A + B + C = 4 -3 + 3 = 4