# What is an example of a linear equation written in function notation?

A function is said to be linear if the dipendent and the indipendent variable grow with constant ratio. So, if you take two numbers ${x}_{1}$ and ${x}_{2}$, you have that the fraction $\frac{f \left({x}_{1}\right) - f \left({x}_{2}\right)}{{x}_{1} - {x}_{2}}$ is constant for every choice of ${x}_{1}$ and ${x}_{2}$. This means that the slope of the function is constant, and thus the graph is a line.
The equation of a line, in function notation, is given by $y = a x + b$, for some $a$ and $b \setminus \in \setminus m a t h \boldsymbol{R}$.