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 $A + B+ C$.

EDIT: I copied the problem wrong

Line thru (-3,-5) and (6,1) in standard form.

Point point form for the line joining (a,b) and (c,d) is

(c-a)(y-b) = (d-b)(x-a)

(6 - -3)(y - -5) = (1 - -5)(x - -  3)

9(y + 5) = 6(x + 3)

9y + 45 = 6x + 18

27 = 6x - 9y

2x - 3y = 9

Ax + By = C

That satisfies the constraints,

A=2, B=-3, C=9

A+B+C=8

8

Check:  2x - 3y = 9  thru (-3,-5) and (6,1)

2(-3)-3(-5)= -6 + 15 = 9 good

2(6) - 3(1) =12 - 3 = 9, good

chiken

step-by-step explanation: