A line passes through the points (-3,-5) and (6,1). The equation of this line can be written 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.
The slope of the line is (6 - (-3))/(1 - (-5)) = 9/6 = 3/2, so by point slope form, the equation of the lins is (y + 5) = 3/2(x + 3). Then 2y + 10 = 3x + 9, so 3x - 2y = 1. A + B + C = 3 + (-2) + 1 = 2.
