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

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.

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

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

Therefore, the given function is linear.

y=3x+4

step-by-step explanation:

given the points a(0,4) and b(-4, -8)

eqn of line ab: (y-4)/(x-0)=(-8-4)/(-4-0)

(y-4)/x=-12/-4=3

y=3x+4