Question

The table shows a function. Is the function linear or nonlinear?
x y
7 16
8 11
9 6
linear or nonlinear

Answer 1

That function is linear because it have exactly one output for each input.

Answer 2

its linear since the change in y values is constant...

Answer 3

Yes, the function is linear and I'll explain why.
The general formula for a linear function is: f(x)= mx +t
So we get the first two points and apply them to the formula:
1. 7m + t = 16
2. 8m + t = 11
So we subtract the second one of the first one:
1-2. 16- 11 = 8m + t - 7m -t
-> 5 = -m
-> -5 = m
in 1. 7 * (-5) + t = 16
-> t = 51
So the formula is: f(x) = -5x + 51
Now we controll this with the last point:
-5 * 9 + 51 = 6
The formula is correct and the table gives us three points of a linear function.
I hope I could help you and I am sorry for my english (not my mother tongue).