5) James and Andrew are considering adding some premium channels to their satellite package. The cost oftheir total bill if they added 1 and 4 premium channels is $45.60 and $66.60, respectively.a) Find the slope.b) Write the equation of the line.c) Determine the base price (with O premium channels).

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 $38.6Step-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