How do you tell if a table represents a linear function?

Choose any two points at random from the table.  Find the slope of the line segment connecting those two points.  Now pick another two points at random, and find the slope again.  Are the two slopes the same?  That's one criterion for assuming that the table represents a linear function.

To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is you're looking at a linear function!