How to tell if a function is linear? 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 linear function is a particular case of the affine function **f(x) = a.x + b**, where **b = 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**

So, to write a linear function in its standard form would be something like **f(x) = a.x**.

## What does a linear function graph look like?

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 de **a** coefficient, the more steep the graph line will be.