Question

What is the starting fee, and what does she pay monthly?

Answer 1

Given that the company charges a starting fee and then also charges a monthly fee, you can identify that the equation that models this situation must be a Linear Equation.

Knowing that:

- After 6 months, Elena will have paid $280 in total.

- After 14 months, she will have paid $560 in total.

You know that these two points are on the line:

`(6,280),(14,560)`

Then, you can find the slope of the line using this formula:

`m=(y_2-y_1)/(x_2-x_1)`

Where these two points are on the line:

`(x_1,y_1),(x_2,y_2)`

In this case, you can set up that:

`\begin{gathered} y_2=560 \\ y_1=280 \\ x_2=14 \\ x_1=6 \end{gathered}`

Therefore, substituting these values into the formula and evaluating, you get that:

`m=(560-280)/(14-6)=(280)/(8)=35`

By definition, the Slope-Intercept Form of the equation of a line is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

You can find the value of "b" by substituting the slope and the coordinates of one of the points on the line into the equation, and then solving for "b":

`280=35(6)+b`
`280-210=b`
`b=70`

In this case, let be "y" the total amount of money Elena pays for the internet service provider, and "x" the number of months.

You can set up this equation to represent the situation:

`y=35x+70`

Where the y-intercept represents the starting fee for Elena's new internet service provider, and the slope represents the monthly fee.

Hence, the answer is:

- Starting fee: $70.00

- Monthly fee: $35.00