Word problem about Cost and Distance

Question

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $402 to drive 380 mi and in June it cost her $602 to drive 880 mi.
(a) Express the monthly cost C as a function of the distance driven, d, assuming that a linear relationship gives a suitable model.

Answer 1

Alex,

 

Assume that the monthly cost is C = md + k (where k and m are constants)

Since it is a linear relationship m is calculated as slope of the 2 points

m = (602-402)/(880-380)

m = 200/500 = 0.4

 

To calculate k substitute for values from first point

402 = (.4)(380) + k

k = 250

 

You can check this with the second point

602 = 0.4(880) + 250

602 = 602

 

So the linear equation is C = 0.4d + 250