How to Tell if a Table is Linear

 You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.
 X Y
 1 2
 2 4
 3 6
 4 8
 This table is linear. the first difference between Y1 & Y2, Y2 & Y3, and Y3 & Y4 is 2. Therefor, 2 is Y's constant rate.
 X Y
 1 6
 2 9
 3 1
 4 40
 This table is NOT linear. The first difference between Y1 & Y2 is 3, Y2 & Y3 is 8, Y3 & Y4 is 39, which means that Y does not increase at a constant rate as X increases by 1. This proves that this relationship is not linear.