## What is an affine function?

An affine function, also known as first degree polynomial function, is a function of f : ℝ→ℝ, defined as the form **y=ax+b** or **f(x) = ax + b**, where **a** and **b** are real numbers and **a ≠ 0, b ≠ 0**.

In this type of functions the **a** is called the coefficient of x and represents the growth rate, variation rate or angular coefficient. The **b** is called the constant term and represents the y-interception.

## What is the graph of an affine function?

The graph of an affine function is a **straight line **that intercepts the **y-axis** in the point **(0, b)**. To plot the graph, one needs to know at least two points.

For example, to plot the graph of **y = 3x + 6**, first it is necessary to calculate the root (or zero) of the function. The root, or zero, is where the function intercepts the **x-axis**, and can be calculated equalizing **y=0**.

3x + 6 = 0 -> x = -2

So, one point is (0, 6) and the other point is (-2, 0).

Having two known points, one can plot the graph such as:

Affine functions can be increasing or decreasing. To know this, one just has to identify the signal of the **a** coefficient. If **a** is positive, the function will be increasing. If **a** is negative, the function will be decreasing.