Q:

Magnitude of the value of a line at a point which does not lie on it

This may be trivial but I had never thought of it before. I know that the sign of the value represents on which side of a line a point lies but don't know what the magnitude of that value represents.
Consider the line $3x+2y+1=0$, at $(-1,-2)$ it evaluates to $-6$, what does $|-6|$ represent?

A:

It doesn't mean anything else unless one introduces more information: One could just as well write the same line as
$$6x + 4y + 2 = 0,$$
but evaluating the l.h.s. at $(-1, -2)$ gives $-12$, which has absolute value $12 \neq 6$.

