Chapter 4.2, Problem 40PPS

a.

To determine

To find: Equation in point slope form of total price $y$ for any number of hours $x$ .

Answer to Problem 40PPS

Point slope form is $\left(y-325\right)=50\left(x-6\right)$

Explanation of Solution

Given information:

Rent of wave runner = $ 50 per hour and service fee.

Total cost of service and rent for 6 hours = $325.

Total cost of service and rent for 6 hours = cost of rent for 6 hours + service fee.

Let us assume service fee be x.

We know

Cost of rent for one hour =$50

  $\begin{array}{l}\Rightarrow 325=6\times 50+x\\ \Rightarrow 325=300+x\\ \Rightarrow x=325-300\\ \Rightarrow x=25\end{array}$

Therefore

Service fee= $25

Total cost of service and rent cost for one hour = cost of rent for one hour +service fee

Total cost of service and rent cost for one hour = $50+25$

Total cost of service and rent cost for one hour = $75

Therefore

We got Two points $\left(6,325\right)$ and $\left(1,75\right)$

Slope = m = $\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}\Rightarrow m=\frac{75-325}{1-6}\\ \Rightarrow m=\frac{-250}{-5}\\ \Rightarrow m=50\end{array}$

Point slope form is $\left(y-y_1\right)=m\left(x-x_1\right)$

  $\begin{array}{l}\Rightarrow (y-325)=50(x-6)\\ \Rightarrow y-325=50x-50\times 6\\ \Rightarrow y-325=50x-300\\ \Rightarrow y=50x-300+325\\ \Rightarrow y=50x+25\end{array}$

Therefore

Point slope form is $\left(y-325\right)=50\left(x-6\right)$

b.

To determine

To find: Equation in Slope intercept form.

Answer to Problem 40PPS

Slope intercept form is $y=50x+25$

Explanation of Solution

Given information:

Rent of wave runner = $ 50 per hour and service fee.

Total cost of service and rent for 6 hours = $325.

Point slope form is $(y-y_1)=m(x-x_1)$

  $\begin{array}{l}\Rightarrow (y-325)=50(x-6)\\ \Rightarrow y-325=50x-50\times 6\\ \Rightarrow y-325=50x-300\\ \Rightarrow y=50x-300+325\\ \Rightarrow y=50x+25\end{array}$

Therefore,

Slope intercept form is $y=50x+25$

c.

To determine

To find: Service fee.

Answer to Problem 40PPS

Service fee= $25

Explanation of Solution

Given information:

Rent of wave runner = $ 50 per hour and service fee.

Total cost of service and rent for 6 hours = $325.

Total cost of service and rent for 6 hours = cost of rent for hours + service fee.

Let us assume service fee be x.

We know

Cost of rent for one hour =$50

  $\begin{array}{l}\Rightarrow 325=6\times 50+x\\ \Rightarrow 325=300+x\\ \Rightarrow x=325-300\\ \Rightarrow x=25\end{array}$

Therefore

Service fee= $25