Answer:
Find the slope for each of the points in the table. If all the slopes equal each other, the table represents a linear function. If not, then it's the opposite.
Explanation:
(You didn't post the full picture, but I'll try to make sense of your problem and answer anyways.)
A linear function, or a line, has a constant slope. This means that no matter where you are on the line, it was always be "rising" some y and "running" some x. It will never be fluctuating in slope or anything like that because it's a line, not a curve, not a zigzag, etc. Just a line.
How do we observe this in tables? Well, remember that the slope m can be found with the following formula:
where (x1, y1) and (x2, y2) are two points on a line.
So, we can show that all these points have equal slopes to see if they form a line. For example, let's look at the table shown in the picture. We have five points, so let's find the slope for two of them at a time.
First, let's find the slope between (1, 5) and (2, 20).
The slope between these two points is 15.
Now, let's find the slope between (2, 20) and (3, 45).
And the slope is ... 25? This can't be right!
Well, it is. This means that these three points can't all form a line, and therefore, all of these points can't form a line. So, the table shown in the picture does not represent a linear function. Do this for the other tables in the question, and you got yourself your answer.