Standard Form of a Line

The standard form of a linear equation is

$Ax+By=C$ .

The advantage of standard form is that it accommodates both horizontal lines $(A=0)$ and vertical lines $(B=0)$ .

The disadvantage is that $A,B,\text{and}C$ do not stand for anything obvious (like the slope or $y$ -intercept ). In fact, they are not unique: if we double them all, we get back the same line! You can check this with the following example.

$\begin{array}{l}x+2y=3\\ 2x+4y=6\end{array}$

These two equations, both in standard form, represent the same line.