Chapter 8.8, Problem 41PPS

(a)

To determine

The slope intercepts form equation and the meaning of the slope from the following table:

Number of people	Total cost $\$$
$3$	$104.85$
$5$	$174.75$

Answer to Problem 41PPS

The system of equation is written as:

  $\begin{array}{l}x+y=5\\ x-y=3\end{array}$

Explanation of Solution

Given:

Number of people	Total cost $\$$
$3$	$104.85$
$5$	$174.75$

Concept Used:

The slope intercept form is:

  $y=mx+b$

Where,

Slope: $m$

  $y$ -intercept: $b$

Calculation:

Consider:

Number of people: $x$

Total cost: $y$

Now, take the data points as:

  $\begin{array}{l}A=\left(x_1,y_1\right)=\left(3,104.85\right)\\ B=\left(x_2,y_2\right)=\left(5,174.75\right)\end{array}$

Now, the slope is calculated as:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{174.75-104.85}{5-3}\\ m=\frac{69.9}{2}\\ m=34.95\end{array}$

So, the slope intercept eq. can be written as:

  $\begin{array}{l}y=mx+b\\ y=34.95x+b\end{array}$

Now, need to put $\left(3,104.85\right)$ in $y=34.95x+b$ :

  $\begin{array}{l}104.85=34.95\left(3\right)+b\\ b=104.85-104.85\\ b=0\end{array}$

So, the final slope-intercept form is $y=34.95x$ .

Conclusion:

Hence, the final slope-intercept form is $y=34.95x$ .

(b)

To determine

The cost of $9$ people to go on the snorkelling trip

Answer to Problem 41PPS

The cost of $9$ people to go on the snorkelling trip is $\$314.55$ .

Explanation of Solution

Given:

Number of people: $x=9$

Calculation:

From the subpart (a):

The final slope-intercept form is expressed as:

  $\begin{array}{l}y=34.95x\\ y=34.95\left(9\right)\\ y=\$314.55\end{array}$

So, the cost of $9$ people to go on the snorkelling trip is $\$314.55$ .

Conclusion:

So, there is $\$314.55$ is required for $9$ people to go on the snorkelling trip.