Suppose $f$ is a real valued function with domain a subset of
real numbers, $D$.

Definition: $f$ is a **linear function** if **there
a numbers $m$ and $b$ so that for any $x \in D$, $f(x) = mx
+b$**

**Comment: **The letters $m$ and $b$ have been used to represent
for these numbers for hundreds of years, but there are alternatives.
Here are two alternatives:

i. __$f$__ is a linear function if there a numbers**
$a_1$ and $a_0$** so that for any $x \in D$, **$f(x) =
a_1 x +a_0$**.

ii. __$f$__ is a linear function if there a numbers
**$A$ and $B$ **so that for any $x \in D$, **$f(x) = Ax
+B$**.

The number **$m$ **is sometimes referred to as "the slope,"
"the rate," or the "linear coefficient " of the linear function.

The number** $b$** is sometimes referred to as "the $y$-
intercept," "the initial value," or the "constant " of the linear
function.