How can you use an equation or a graph to decide if a function is linear?

An equation can be determined as linear if it is first order in a single variable, i.e. y=3x, but not y=3x^2.
A graph will be linear if the slope is constant

Here is the standard form of a linear equation in two variables 
Ax + By = C Look at the x. The exponent is understood to be 1. Look at the y. The exponent is understood to be 1. 

x − 3y = 2 is a linear equation since the exponents of x and y are both one.

1/x+y=9is not a linear equation since x is in the denominator of thefraction.

If you make it a little more clear i can answer it