Question

Which table represents a linear function?

Answer 1

The last table show a linear equation

Answer 2

In each table, x increases by 1. We start with x = 0 and stop with x = 3. So we will focus on the y columns of each table as those are different.

Let's move from left to right along the four tables.

For the first table, we go from y = 1 to y = 2. That's an increase of 1
Sticking with the first table, we go from y = 2 to y = 4. The increase is now 2
Since the increase is not the same, this means the table is not linear. The y increase must be constant. We can rule out choice A

Choice B can be ruled out as well. Why? Because...
the jump from y = 0 to y = 1 is +1
the jump from y = 1 to y = 3 is +2
The same problem comes up as it did with choice A

Choice C has the same problem, but the increase turns into a decrease half the time. We go from y = 0 to y = 1, then we go back to y = 0 so the "increase" is really a decrease. We can think of it as a negative increase. Regardless, this allows us to rule out choice C

Only choice D is the answer. Each time x goes up by 1, y goes up by 2. Therefore the slope is 2/1 = 2