The King-Altman method of deriving rate equations for enzymatic reactions is applied to the derivation of the Michaelis-Menten equation, along with an explanation for how (or why) the King-Altman method works in this case. The slightly more complicated cases of competitive inhibition and a two-substrate enzyme-catalyzed reaction are then treated in the same manner. It is the intent of the author that through this process of seeing how the King-Altman method works in progressively more complicated cases, a student is in a better position to appreciate the generality of the method and, perhaps, the general proof of the method. (Contains 3 figures.)