Question

5) James and Andrew are considering adding some premium channels to their satellite package. The cost of

Answer 1

Answer:

Part (A): The slope is 7.

Part (B): The required equation of line is $y=7x+38.6$.

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.

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

Substitute $(x_1,y_1)=(1, 45.60)$ and $(x_2,y_2)=(4, 66.60)$ in above formula.

$m=\frac{66.60-45.60}{4-1}$

$m=\frac{21}{3}=7$

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: $(y-y_1)=m(x-x_1)$

Substitute the respective values in the above formula.

$(y-45.60)=7(x-1)$

$y-45.60=7x-7$

$y=7x+38.6$

Hence, the required equation of line is $y=7x+38.6$.

Part (C) Determine the base price (with O premium channels)

Substitute x=0 in $y=7x+38.6$.

$y=7(0)+38.6$

$y=38.6$

Hence, the base price is $38.6