How do you tell the differences between a linear and nonlinear equation?

A linear equation has every variable occurring only to the first power in terms involving only one variable at a time, and possibly constants. Every term has degree one or zero.
Examples include x=3 or y=-2 which are linear in one variable, y=2x+3 or 2x-3y=6 which are linear in two variables, x+y+3z=-10 which is linear in three variables etc...
The graphs of linear equations are lines (hence the name.) For linear equations of two variables, there is a constant rate of change called the slope -- as one variable changes by a fixed increment, the other variable will also change by a fixed increment (not necessarily the same.)
A nonlinear equation has a term or terms with degree greater than one, or a negative or rational (non-integral) power.
Examples include y=x^2, y=1/x, y=x^(2/3), y=x^3-x ,z=xy .Note that z=xy is not linear as the xy term has degree two. Transcendental functions (e.g. trigonometric, logarithmic, etc...) are not linear.
The graphs of nonlinear equations involve curves.
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