Chapter 8.6, Problem 7E

To determine

What is the approximate length of a butter clam that is 85 millimeters wide?

Answer to Problem 7E

The length of a butter clam that is 85 millimeters widewould be approximately109 millimeters.

Explanation of Solution

Given:

The table shows the dimensions of seven butter clams.

  

Calculation:

First of all, we will plot our given values on coordinate plane and draw a line of best fit as shown below:

  

Our next step is to write the equation of line of best fit.

Let us find slope of line passing throughpoints (13,17) and (71,91) as:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{91-17}{71-13}\\ m=\frac{74}{58}\\ m=\frac{37}{29}\end{array}$

Now we will use point-slope form to write our equation as:

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-17=\frac{37}{29}(x-13)\\ y-17=\frac{37}{29}x-\frac{481}{29}\\ y=\frac{37}{29}x+\frac{12}{29}\end{array}$

To predict the length of a butter clam that is 85 millimeters wide, we will substitute $x=85$ in equation of line of best fit as:

  $\begin{array}{l}y=\frac{37}{29}x+\frac{12}{29}\\ y=\frac{37}{29}(85)+\frac{12}{29}\\ y=\frac{3157}{29}\\ y=108.86206\\ y\approx 109\end{array}$

Therefore, the length of a butter clam that is 85 millimeters wide would be approximately 109 millimeters.