###### Definition 4.7.2 Standard Form

It is always possible to write an equation for a line in the form

\begin{equation}
Ax+By=C\tag{4.7.1}
\end{equation}

where \(A\text{,}\) \(B\text{,}\) and \(C\) are three numbers (each of which might be \(0\text{,}\) although at least one of \(A\) and \(B\) must be nonzero). This form of a line equation is called standard form. In the context of an application, the meaning of \(A\text{,}\) \(B\text{,}\) and \(C\) depends on that context. This equation is called standard form perhaps because *any* line can be written this way, even vertical lines which cannot be written using the two previous forms we've studied.