To check if table does represent linear function, just check for each increment in x, y increase by constant value.
Example:
x y
1 2
2 4
3 6
4 8
When you go from x=1 to x=2, you will see that y goes from 2 to 4, so that's 2 units increase.
When you go from x=2 to x=3, y goes from 4 to 6. That's still 2 units increase.
Finally, from x=3 to x=4, y goes from 6 to 8, still 2 units increase, so since unit increase is same, it represents linear function.
So for first table, y goes from 3 to 7, that's 4 units. Then 7 to 11, that is also 4 units. 11 to 15, still 4 units. So it is linear function.
Second is not linear because y=3 to y=8 is increase in 5 but y=8 to y=15 is 7 units increase.
Third is not linear because y increases then decreases.
Fourth is not linear because it increase faster and faster.
So correct answer is first table
x y
1 3
2 7
3 11
4 15
Hope this helps.