My question is from chapter 1, section 2.3 of the book "Complex analysis" written by Lars-Ahlfors. The book mentions that a direct line $z=a+bt$ determines a right half plane of $Im(\frac{z-a}{b})<0$ and left half plane of $Im(\frac{z-a}{b})>0$.
I have no idea how the above formula comes. The only thing I know is that for $s$ in right half plane, assume the curve has positive slope, $Im(s)<z=a+bt$ and $Re(s)>z$.