We can check if a table is a linear function by comparing the rate of change on variables x and y, and if the rate is the same for the x column and the rate is the same for the y column, then the table represents a linear function. In this case, we have the following:
notice that on the first table, we dont have on either column that the rate is constant, and on the second table the rate is constant on the column x,but it is not on the column y, therefore, these two tables don't represent a linear function.
For the next two tables,we have the following:
as we can see, none of these tables are linear functions.