Chapter 8, Problem 1E

(a)

To determine

To write: linear equation for the given data.

Answer to Problem 1E

The equation of line of fit is $y=26x+28$

Explanation of Solution

Given:

  

Calculation:

Write the equation to represent the data

Now, find the slope using points $\left(2,80\right)$ & $\left(4,132\right)$

  $\begin{array}{c}m=\frac{132-80}{4-2}\\ =\frac{52}{2}\\ =26\end{array}$

Now, write the equation using slope intercept form $y-y_1=m\left(x-x_1\right)$

Substitute the values $m=26$ and point $\left(2,80\right)$

  $\begin{array}{c}y-80=\left(26\right)\left(x-2\right)\\ =26x-52\end{array}$

Adding 80 on both sides

  $y=26x+28$

Therefore, the equation of line of fit is $y=26x+28$

Conclusion:

Therefore, the equation of line of fit is $y=26x+28$

(b)

To determine

To describe: the meaning of slope

Answer to Problem 1E

The total cost of the job per number of hours J takes to do the job

Explanation of Solution

The slope represents here the total cost of the job per number of hours J takes to do the job

(c)

To determine

To find:the total cost of the job

Answer to Problem 1E

The total cost of the job if it takes for J 7 hours is $210

Explanation of Solution

Calculation:

Find the total cost if J take 7 hours for job

Substitute the value of $x=7$ in equation $y=26x+28$

  $\begin{array}{c}y=26\left(7\right)+28\\ =182+28\\ =210\end{array}$

Therefore, the total cost of the job if it takes for J 7 hours is $210

Conclusion:

Therefore, the total cost of the job if it takes for J 7 hours is $210