The line $l_1$ passes through the points $(3,-3)$ and $(-5,2)$. The line is the graph of the equation $Ax + By = C$, where $A$, $B$, and $C$ are integers with greatest common divisor 1, and $A$ is positive. Find $A + B+ C$.
The slope of line l_1 is (-5 - 3)/(2 - (-3)) = -8/5. Then by point-slope form, the equation is
y + 3 = -8/5 (x + 3)
Multiply by 5:
5y + 15 = -8(x + 3)
Expand:
5y + 15 = -8x - 24
Simplify:
8x + 5y = -39
Then A + B + C = 8 + 5 + (-39) = -26.