== Relationship with other classes of functions ==
Linear functions are a particular kind of [[polynomial]]s. If the coefficient on the variable is not zero ({{math|''A'' ≠ 0}}), then it is a [[degree of a polynomial|degree]] 1 polynomial (also called a ''linear polynomial''), otherwise it is a [[constant function]] –. also a polynomial, but of lower degree.
A linear function also representsrepresent an [[exponentialExponential growth|exponential function]] whose [[codomain|values]] are expressed in the [[logarithmic scale]]. It means that when {{math|[[logarithm|log]](''g''(''x''))}} is a linear function of {{mvar|x}}, the function {{mvar|g}} is exponential. With linear functions, increasing the input by one unit causes the output to increase by a fixed amount, which is the slope of the graph of the function. With exponential functions, increasing the input by one unit causes the output to increase by a fixed multiple, which is known as the base of the exponential function. If ''both'' [[___domain of a function|arguments]] and values of a function are in the logarithmic scale, then a linear function represents a [[power law]]:
:<math>\log_r y = A \log_r x + B \quad\Rightarrow\quad y = r^B\cdot x^A</math>
