Application problem with a linear function: Finding a coordinate given two points

Question

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 30

 minutes of calls is $12.53

 and the monthly cost for 77

 minutes is $18.64

. What is the monthly cost for 37

 minutes of calls?

Answer 1

(30, 13.53) and (77, 18.64) are two points on a line with slope = (18.64- 13.53)/(77-30) = 5.11/47

y -13.53 = (5.11/47)(x-30)

y = 5.11x/47 - 153.3/47 + 13.53

y =5.11x/47 + 482.91/47

y = 5.11(37)/47 + 482.91/47 = about $14.30

37 is 7 more than 30

37 is 40 less than 77

18.64-13.53 = 5.11

7/47)(5.11) = 35.77/47 = .76

.76 + 13.53 = 14.29