Question

Which of the following describes the graph of a linear function?

A) It is V shaped and it passes through the origin.

B) It is a straight line in one portion and a curve in another portion.
C) Its y-values decrease at a constant rate as its x-value decreases.
D) Its y-values increase at a nonconstant rate as its x-value increases.

Answer 1

A linear function is a straight line so its fairly easy to select the correct answer

Answer 2

While all linear equations produce straight lines when graphed, not all linear equations produce linear functions. In order to be a linear function, a graph must be both linear (a straight line) and a function (matching each x value to only one y-value). It must also pass a polygraph test, complete an obstacle course, and provide at least three references. The qualifications are stringent.

Any equation of the form

y = (constant)

will give us a linear function.

Any equation of the form

x = (constant)

is a linear equation but does not describe a function. Remembering the absolute nonsense words "yunction" and "xquation" should help you keep things straight.