Question

By your cell phone contract, you pay a monthly fee plus some money toreau month, you spent 260 minutes on the phone, and paid $22.10. In another month, you spent 330 minutes on the phone, and paid $24.55. What is the rate (in dollars per minute) that the phone company is charging you? That is, what is the slope of the line if you ploited the bill versus the number of minutes spent on the phone? The rate is per minute

Answer 1

Recall that we are told that the cell phone company charges a fixed monthly fee plus a fee that depends on how many minutes you use the phone during the month. If we let b be the fixed charged fee and m be the rate (dollars per minute) that the company charges, then, the total amount charged if we use x dollars in the month, would be

`y=mx+b`

which corresponds to the equation of a line. We want to calculate m, which is the slope of this line. We know that if we use the phone 260 minutes, we get a bill of 22.10. Also, we know if we spent 330, we are charged 24.55. If we translate into our variables, that means that whenever x=260 we get y=22.10 and if x=330 we get y=24.55. We can summarize this using the coordinates as (260,22.10) and (330,24.55).

Recall that, to calculate the slope that joins the points (a,b) and (c,d), we use the formula

`m=\frac{d\text{ -b}}{c\text{ -a}}=\frac{b\text{ -d}}{a\text{ -c}}`

In our case, we have a=260, b = 22.10, c=330, d=24.55. So, the slope of the line that we want would be

`\frac{24.55\text{ - 22.10}}{330\text{ -260}}=(2.45)/(70)=0.035`

so the company charges 0.035 dollars per minute