## What is a linear function?

A linear function is a first degree polynomial function and a particular case of the affine function **f(x) = a.x + b**, where **b = 0**. A linear function is a function of f : ℝ→ℝ defined as **f(x) = a.x**, where **a** is a real number and **a ≠ 0. **

The **a** number that multiplies by **x**, is called the **coefficient** of the function. When the **coefficient = 1**, the linear function will be called as the **identity function**, **f(x) = x**

## What is the linear function graph?

The graph of a linear function is a straight line that crosses the origin, thus, the point (0, 0). The **a** coefficient indicates the slope or steepness of the line. The higher **a** coefficient, the more steep the graph line will be.

Linear 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.

## How to graph linear functions?

To plot the graph of a linear function, it is necessary to know, at least, two points. One of the points is (0, 0) and the other point can be calculated, as the following example:

Given the function **f(x) = 2.x**

To be easier, one can build a table by giving values to** x** and calculate de values of **f(x)**, obtaining points to plot the graph. One point is already known, is the (0, 0) point.

if x = 1 then, f(x) = 2