Find a linear equation for y, the monthly cost in dollars, of the cell plan as a function of x, the number of monthly minutes used

Question

A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 390 minutes, the monthly cost will be $78.50. If the customer uses 860 minutes, the monthly cost will be $149.(a) Find a linear equation for y, the monthly cost in dollars, of the cell plan as a function of x, the number of monthly minutes used.

y = 

(b) Interpret the slope and y-intercept of the equation.

The  ---Select--- y-intercept slope is the $  flat monthly fee, and the  ---Select--- y-intercept slope is the $  fee for each additional minute used.

(c) Use your equation to find the total monthly cost if 438 minutes are used.

Answer 1

78.5=390m+b

149 = 860m +b

subtract to get

149-78.5 = 860m -390m

70.5 = 470m

m = 70.5/470 = 705/4700 = 175/940=35/188

b = 78.5 - 390(35/188) = 78.5 - 72.6 = about $5.90 monthly fixed fee

a) y = 35x/188 + 5.9

b) slope = 35/188 = cost per minute (without the monthly fee) = about 19 cents per minute

y intercept = about $5.90 = the monthly fee which applies regardless how many minutes are used

c) 438 minutes costs 5.9+ 35(438)/188 = about $87.44