The conventional representation of a linear function as $f(x) = mx + b$ can sometimes be missing in applications, but that omission cannot diminish its importance. Visualizing these applications with cartesian graphs sometimes is also missed. In this section we highlight a few of the more elementary applications and their visualization with mapping diagrams.

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Speed (Velocity)

Scales

Direct Proportion

Rates

A standard form of a linear equation with variable $x$ is an equation of the form $Ax + B = C$ with $A \ne 0$.

Beginning algebra spends a considerable amount of time solving this equation without any reference to functions.

When $B = 0$ this equation has the solution $x = \frac C A$.

When $B \ne 0$ the equation can be solved so that $x = \frac {C- B} A$.