Often students feel they understand a formula and understand a picture, but have difficulty going back and forth between the two languages describing the same thing.  Our development of the interaction between linear and nonlinear equations and graphs is based on vector algebra and geometry.  Basic vector geometry and algebra is not only a helpful way to understand the equations of calculus, it is a powerful tool in many parts of math, science and engineering.  We urge our reader to develop a working lexicon (or "translation dictionary") that contains the equivalent "words" of the two languages.