Question

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

x	$y=f\left(x\right)$
-2	8
-1	8
0	8
1	8
2	8

Short answer

The function is linear and the equation of the line is$f\left(x\right)=8$

Step-by-step solution

Step 1. Given Information  

The given data is

x	$y=f\left(x\right)$
-2	8
-1	8
0	8
1	8
2	8

The data in the table represent values ofy with respect tox.

Compute the average rate of change of each function.

• If the average rate of change is constant, then the function is linear.
• If the average rate of change is not constant, then the function is nonlinear.

Step 2. Calculation  

Calculate average rate of change by the formula$\frac{∆y}{∆x}=\frac{y_2-y_1}{x_2-x_1}$

x	y	$\frac{∆y}{∆x}$
-2	8	0
-1	8	0
0	8	0
1	8	0
2	8

The average rate of change is constant, so the function is linear.

Step 3. Find equation of line.  

The average rate of change is $m=0$and a point from given data $(-2,8)$.

Use slope point form to find equation of the line.

$$\begin{gathered} y-y_1=m(x-x_1) \\ y-8=0(x-(-2\left)\right) \\ y-8=0 \\ y=8 \end{gathered}$$

Step 4. Conclusion  

As average rate of change is constant, so function is linear and the equation of the line is $f\left(x\right)=8$