Express the equation of the line passing through points $(1,7)$ and $(-2,-3)$ in the form $ax+by=c$, where $a$, $b$ and $c$ are integers, the greatest common divisor of $a$ and $b$ is 1, and $c<0$.
$(1,7)$ and $(-2,-3)$
Slope = [ -3 - 7 ] / [ - 2 - 1] = -10 / - 3 = 10 / 3
Equation of the line passing through these points =
y = (10/3) (x - 1) + 7
y = (10/3)x - 10/3 + 7
y= (10/3)x +11/3 multiply through by 3
3y = 10x + 11 rearrange as
10x - 3y = -11
