00:01
This problem says which of these tables represents a linear function, and to be able to determine which one is a linear function, we need to remember a key characteristic about linear functions, and that is that our rate of change for a linear function is considered constant.
00:18
So that means that assuming that our x values are increasing or decreasing by the same value each time in our chart, that as long as our y values are either increasing by the same number or decreasing by the same number, then we have something that's a linear function.
00:32
But if that increase or decrease changes at all as far as the value, then it would not be considered linear.
00:36
And looking at all of our x values, we're going from 3 to 4 to 5 to 6 for all three tables, so that means that we can just focus on the y values because the increase for x is constant as a plus 1.
00:48
And for our first possibility for our function, we see 3 going to 4, which is an increase of 1, but then we see 4 going to 6, which is an increase of 2, and then 6 goes to 7, which is an increase of 1 again.
01:01
This increase did not stay constant, so our first table wouldn't be considered linear...