Equation:
\[
   ax+by=c
\]

$c=ax_0+by_0$:

\[
   a(x-x_0)+b(y-y_0)=0
   \quad\Leftrightarrow\quad
   \underline{n} \cdot \overrightarrow{P_0P}=0
   \quad\Leftrightarrow\quad
   \underline{n} \perp \overrightarrow{P_0P}
\]