Who do you know if the table or equation is a linear function or non-linear function?

For a table you can just plot the points and graph them out, if the line is straight that means it's linear. If it curves in any shape or form (not straight) then it's non-linear.

For equations it's all about the LEADING TERM (Or the term with the highest power) if the leading term is just an x or y without any powers attached to them then you've got yourself a linear equation. However if the leading term has a power associated with itself then it's going to be non-linear.

Here are some examples:

(x - 2) = y     LINEAR

x^2 + 6 = 4y    NON-LINEAR

(x + 6)^3 = y    NON- LINEAR

9001x (ITS OVER 9000) + 420y = 1   LINEAR

Hope this helped. 

If you are unable to plot them then take the differences of successive y-values and divide by the corresponding differences of the x-values.  If the resulting values are all the same they represent a linear function, otherwise they represent a non-linear function.