Chapter 4.3, Problem 36PPS

To determine

The equation in point-slope form to find the total price $\left(y\right)$ for the number of months $\left(x\right)$ .

Answer to Problem 36PPS

The equation in point-slope form for the total price $\left(y\right)$ for the number of months $\left(x\right)$ is $y-264.70=39.95\left(x-6\right)$

Explanation of Solution

Given: It is given that the company offers premium cable $39.95 per month plus one time setup fee say $\left(c\right)$ . And the total cost $\left(y\right)$ for setup and 6 months of service is $264.70. Therefore, the relation between the total cost $\left(y\right)$ and the number of months $\left(x\right)$ for the setup fee $\left(c\right)$ is written as,

  $y=39.95x+c\mathrm{......}\left(1\right)$

Calculation:

From (1)the slope is 39.95 and the point is $\left(6,264.70\right)$ . Now, the relationship between the total cost $\left(y\right)$ and number of months $\left(x\right)$ can be evaluated as,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-264.70=39.95\left(x-6\right)\mathrm{......}\left(\begin{array}{l}\text{Here }m=39.95\text{ and}\\ \left(x_1,y_1\right)\to \left(6,264.70\right)\end{array}\right)\\ y-264.70=39.95\left(x-6\right)\mathrm{......}\left(2\right)\end{array}$

To determine

The equation in slope-intercept form for the number of months $\left(x\right)$ and the total cost $\left(y\right)$ .

Answer to Problem 36PPS

The slope-intercept form for the number of months $\left(x\right)$ and the total cost $\left(y\right)$ is $y=39.95x+25$ .

Explanation of Solution

Given: It is given that the company offers premium cable $39.95 per month plus one time setup fee say $\left(c\right)$ . And the total cost $\left(y\right)$ for setup and 6 months of service is $264.70.

Calculation:

Using (2)the relation between the number of months $\left(x\right)$ and total cost $\left(y\right)$ in slope-intercept form is evaluated as,

  $\begin{array}{l}y-264.70=39.95\left(x-6\right)\\ y-264.70=39.95x-6\times \mathrm{39.95......}\left(\text{Simplifying}\right)\\ y-264.70=39.95x-239.70\\ \text{or, }y=39.95x+\mathrm{25......}\left(\text{Slope intercept form}\right)\end{array}$

To determine

The value of setup fee $\left(c\right)$ .

Answer to Problem 36PPS

The value of setup fee is $25.

Explanation of Solution

Given: It is given that the company offers premium cable $39.95 per month plus one time setup fee say $\left(c\right)$ . And the total cost $\left(y\right)$ for setup and 6 months of service is $264.70.

Calculation:

From (1), the slope $\left(m=39.95\right)$ and the point $\left(6,264.70\right)$ lies on (1). Therefore satisfying point $\left(6,264.70\right)$ in (1) the setup fee $\left(c\right)$ is evaluated as,

  $\begin{array}{c}\left(264.70\right)=39.95\left(6\right)+c\mathrm{......}\left(\text{From }\left(1\right)\right)\\ \text{or, }c=264.70-239.70\\ c=25\end{array}$