A line passes through the points $P$ and $Q.$ If $P = (-8,2)$ and $Q = (1,7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

Question

A line passes through the points $P$ and $Q.$  If $P = (-8,2)$ and $Q = (1,7),$ then write the equation of this line in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive.

GPT 3.5 · Answer

The slope of this line is $$\frac{7 - 2}{1 - (-8)} = \frac{5}{9}.$$The line passes through $(1,7),$ so the equation of the line is $$(y - 7) = \frac{5}{9} (x - 1).$$Multiplying both sides by 9, we get $$9y - 63 = 5x - 5.$$Thus, the equation is $5x - 9y = 58,$ so $A = \boxed{5},$ $B = -9,$ and $C = 58.$