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=(y_2-y_1)/(x_2-x_1)`

`m=(-3-0)/(4-1)=(-3)/(3)=-1`

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

`m=(-6-(-3))/(7-4)=(-6+3)/(3)=(-3)/(3)=-1`

`m=(-9-(-6))/(10-7)=(-9+6)/(3)=(-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.