Linear vs non-linear equations

A linear equation is any equation which graphs a straight line and is of the form

Ax + By = C where A and B are not equal to zero.

examples:
3x + 5y = 8
(4/3)x + 6y = 0
x = 19

These are all linear equations.

Non-linear equations will not be a straight line, and are generally less intuitive, examples are

x^3 + 4y = 8 (this is exponential)

(5/x) + 3y = 9 (contains a variable in the denominator)

2xy = 8 (is multiplicative)