What is the difference between affine and linear functions? An affine function is the composition of a linear function with a translation. So while the linear part fixes the origin, the translation can map it somewhere else.

Affine functions are of the form **f(x)=ax+b**, where **a ≠ 0** and **b ≠ 0 **and linear functions are a particular case of affine functions when **b = 0** and are of the form **f(x)=ax. **Therefore, one can say that linear functions are also affine functions.

But, the **difference between affine and linear** functions is that linear functions cross the origin of the graph at the point (0 , 0) while affine functions do not cross the origin.

In the example below, the blue line represents an affine function and the red line represents a linear function.