By your cell phone contract, you pay a monthly fee plus some money for each minute you use the phone during the month. In one month, you spent 200 minutes on the phone, and paid $22.45. In another month, you spent 350 minutes on the phone, and paid $29.65.

Question

Let x be the number of minutes you talk over the phone in a month, and let y be your cell phone bill for that month. Use a linear equation to model your monthly bill based on the number of minutes you talk over the phone.

1. This linear model’s slope-intercept equation is?

2. If you spent 110 minutes over the phone in a month, you would pay how much?

3. If in a month, you paid $34.10
of cell phone bill, you must have spent how many minutes on the phone in that month?

Answer 1

1. Y = Co + C*x.
22.45 = Co + C*200,
Co = 22.45 - 200C.

29.65 = Co + C*350.
Co = 29.65 - 350C. = 22.45 - 200C
150C = 7.20, C = 0.048/min.

Co = 22.45 - 200*0.048 = $12.85/mo. = Initial cost.

Y = 0.048x + 12.85.

2. Y = 0.048*110 + 12.85 = $18.13.

3. 34.10 = 0.048x + 12.85, X = ?.