How do you know when an equation is a linear equation?

Answer 1

There are two uses of the word "linear" in math. The first is simple: linear function is one who's graph is a straight line. This happens when the highest power of a polynomial x is 1, ie no terms with x^2 or x^3 or higher (or lower than 1), only x^1 (just x).

Another use of linear-

A function is also said to be "linear" if it has the following properties: (1) Additivity, ie f(x+y) = f(x) + f(y)

(2) f(c*x)=c*f(x), where c is a constant