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.