The monthly cost of driving a car depends on the number of m

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $370 to drive 300 mi and in June it cost her $462 to drive 760 mi. (a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model.

C(d) =

Solution

may

cost = $ 370 , distance = 300mi

june

cost = $ 462 , distance = 760 mi

therefore, there are two points given ( 300,370) and ( 760,462)

slope = y2-y1 / x2 - x1 = 462-370 / 760-300 = 92 / 460 = 1/5

standard linear equation is given by

C(d) = md + b

where, m = slope

plugging the value of one point and slope

370 = 300(1/5) + b

b = 310

hence , linear equation becomes

C(d) = (1/5 )d + 310