Question

Is the function represented by the table linear or nonlinear and why?

x y
2 10
4 9
6 8
8 7


The function is linear because it decreases at a constant rate.

The function is not linear because there is no x value of 0.

The function is linear because all of the values on the table are positive.

The function is not linear because the x values and y values are increasing in opposite directions.

Answer 1

You must find the change in y divided by the change in x, the rate of change, for the given data points.

dy/dx=(9-10)/(4-2)=(8-9)/(6-4)=(7-8)/(8-6)=k=m=-1/2

Since the rate of change is constant this is a linear function.

So as your answer choices put it, it is linear because it decreases at a constant rate.