Chapter 3, Problem 5RE

In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

5.

To determine

We have to determine whether the given function is linear or non linear. If it is linear, then we have to determine the equation of the line.

Answer to Problem 5RE

Solution:

The given function is non-linear.

Explanation of Solution

Given:

The given function is

Formula used:

A function is said to be linear, if it has a constant average rate of change otherwise the function is non-linear.

The formula for finding the average rate of change is

$Avg=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

We know that the average rate of change of a linear function is the slope of that function.

Therefore, we can find the equation of the line using the point-slope formula.

Thus, we get

$y-y_1=m(x-x_1)$

Calculation:

Now, we have to find the average rate of change.

The rate of change between the first and the second row is

$Avg=\frac{-3-4}{-1-(0)}=7$

The rate of change between the second and the third row is

$Avg=\frac{4-7}{0-(1)}=3$

Here, we can see that the rate of change of the given function differs.

Therefore, the average rate of change is not a constant.

Thus, the given function is non-linear.