In order to have a linear relationship, each unitary increase in x will always cause the same increase in y.
So looking at each table, we have:
A.
x from 0 to 1: y increased by 0
x from 1 to 2: y increased by -1.
We can already see that the increase in y was different, so this table does not represent a linear relationship.
B.
x from 0 to 1: y increased by 6
x from 1 to 2: y increased by 6
x from 2 to 3: y increased by 6
x from 3 to 4: y increased by 6
In this table the increase in y was constant, so this table represents a linear relationship.
C.
x from 0 to 1: y increased by -1
x from 1 to 2: y increased by -2
This table doesn't represent a linear relationship.
D.
x from 0 to 1: y increased