Why do we represent linear equations in more than one form?

For two main reasons. 
The first reason is that, depending on the information that is available to you, one or the other is easy to find. 
The second reason is that different forms are "better" in different situations. The slope and intercept are parameters that have very obvious interpretations in 2- dimensional geometry (in 3-D they don't make such obvious sense). 
Hope that helps & Makes sense ! (: