Answer:
Part (A): The slope is 7.
Part (B): The required equation of line is
.
Part (C): The base price is $38.6
Step-by-step explanation:
Consider the provided information.
The cost of their total bill if they added 1 and 4 premium channels is $45.60 and $66.60, respectively.
For 1 premium channel they need to pay $45.60.
This can be written as: (1, 45.60)
For 4 premium channel they need to pay $66.60.
This can be written as: (4, 66.60)
Part (A) Find the slope.
![Slope=m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=Slope%3Dm%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Substitute
and
in above formula.
![m=\frac{66.60-45.60}{4-1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B66.60-45.60%7D%7B4-1%7D)
![m=\frac{21}{3}=7](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B21%7D%7B3%7D%3D7)
Hence, the slope is 7.
Part (B) Write the equation of the line.
By using one of the point and slope we can write the equation of line.
Point slope formula: ![(y-y_1)=m(x-x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%3Dm%28x-x_1%29)
Substitute the respective values in the above formula.
![(y-45.60)=7(x-1)](https://tex.z-dn.net/?f=%28y-45.60%29%3D7%28x-1%29)
![y-45.60=7x-7](https://tex.z-dn.net/?f=y-45.60%3D7x-7)
![y=7x+38.6](https://tex.z-dn.net/?f=y%3D7x%2B38.6)
Hence, the required equation of line is
.
Part (C) Determine the base price (with O premium channels)
Substitute x=0 in
.
![y=7(0)+38.6](https://tex.z-dn.net/?f=y%3D7%280%29%2B38.6)
![y=38.6](https://tex.z-dn.net/?f=y%3D38.6)
Hence, the base price is $38.6