Respuesta :
Answer:
Part (A): The slope is 7.
Part (B): The required equation of line is [tex]y=7x+38.6[/tex].
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.
[tex]Slope=m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute [tex](x_1,y_1)=(1, 45.60)[/tex] and [tex](x_2,y_2)=(4, 66.60)[/tex] in above formula.
[tex]m=\frac{66.60-45.60}{4-1}[/tex]
[tex]m=\frac{21}{3}=7[/tex]
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: [tex](y-y_1)=m(x-x_1)[/tex]
Substitute the respective values in the above formula.
[tex](y-45.60)=7(x-1)[/tex]
[tex]y-45.60=7x-7[/tex]
[tex]y=7x+38.6[/tex]
Hence, the required equation of line is [tex]y=7x+38.6[/tex].
Part (C) Determine the base price (with O premium channels)
Substitute x=0 in [tex]y=7x+38.6[/tex].
[tex]y=7(0)+38.6[/tex]
[tex]y=38.6[/tex]
Hence, the base price is $38.6
