Which table represents a linear function?

For it to be a linear equation, the same difference in x must produce the same difference in y always.

Choice A.
difference in x: 2 - 1 = 1
difference in y: -6 - (-2) = -4

difference in x: 3 - 2 = 1
difference in y: -2 - (-6) = 4

A difference of 1 in x gave a difference of -4 in y and another difference of 1 in x gave a difference of 4 in y.
This is not linear.

Choice B.
difference in x: 2 - 1 = 1
difference in y: -5 - (-2) = -3

difference in x: 3 - 2 = 1
difference in y: -9 - (-5) = -4

A difference of 1 in x gave a difference of -3 in y and another difference of 1 in x gave a difference of -4 in y.
This is not linear.

Choice C.
difference in x: 2 - 1 = 1
difference in y: -10 - (-2) = -8

difference in x: 3 - 2 = 1
difference in y: -18 - (-10) = -8

Do the other differences. All differences in y are -8 corresponding to a difference in x of -1.

This is linear.

Choice D.
The differences in y vary. It is not linear.

Choice C is linear.