Chapter 8.6, Problem 32E

a.

To determine

To show:

The table represents a linear function.

Answer to Problem 32E

The table represents a linear function.

Explanation of Solution

Given:

The table below gives the length of a spring when different masses are suspended from it.

  

Calculation:

To show whether our given table represents a linear function or not, we will see if the values in table has a constant rate of change.

We can see from our table that as x increases by 50 units, y increases by 30 units.

Since the given table has a constant rate of change that is equal to $\frac{30}{50}=0.6$ . Therefore, the given table represents a linear function.

b.

To determine

To write:

An equation forthe function.

Answer to Problem 32E

The equation for the function would be $y=0.6x+80$ .

Explanation of Solution

Given:

The table below gives the length of a spring when different masses are suspended from it.

  

Calculation:

We figured out in part (a) that rate of change for our given table is 0.6, so slope of our line would be 0.6.

We can see from table that the value of y is 80 at $x=0$ , so the y-intercept is 80.

Now we will use slope intercept form of equation to write our function as:

  $\begin{array}{l}y=mx+b\\ y=0.6x+80\end{array}$

Therefore, our required equation would be $y=0.6x+80$ .