Question

Use average rates of change to determine if the function in the table is Linear or Non-linear.

Answer 1

We have been given a table of values of a function. We are asked to determine whether the given function is linear or nonlinear.

We know that a function is linear when its rate of change (slope) is constant.

Let us find slope for each of the given points using slope formula.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-3-0}{4-1}=\frac{-3}{3}=-1$

Similarly, we will find the slopes using other given coordinates.  

$m=\frac{-6-(-3)}{7-4}=\frac{-6+3}{3}=\frac{-3}{3}=-1$

$m=\frac{-9-(-6)}{10-7}=\frac{-9+6}{3}=\frac{-3}{3}=-1$

Since the rate of change for each set of points is $-1$, so the rate of change is constant.

Therefore, the given function is linear.