# Linear Functions

A function is a mathematical machine that takes an input and returns an output. The humble linear function is simple yet one of the most important functions in mathematics. Below are examples of several linear functions:

$$y = 3x+2$$

$$f(x) = -2x+4$$

$$g = 3h+6$$

Notice anything in common? They all have the form:

$$y = mx + b$$

where $m$ and $b$ are numbers.