2.3 Linear Functions

Introduction The notion of a line plays an important role in the study of differential calculus. There are three types of lines in the xy- or Cartesian plane: horizontal lines, vertical lines, and slant or oblique lines. We will see in this section that an equation of each of these lines stems from a linear equation in two variables

where A, B, and C are real constants. The characteristic that gives (1) its name linear is that the variables x and y appear only to the first power. We will refer back to (1) when we review lines and their equations, but let’s note the cases of special interest:

The first and the third of these three equations define functions. By relabeling –C/B in (2) as b we get a constant function.