Question

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

Answer 1

We can do more than giving an example of a linear equation: we can give the expression of every possible linear function.

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 `{f(x_1)-f(x_2)}/{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=ax+b`, for some `a` and `b \in \mathbb{R}`.