why does a linear function give a suitable model in this situation??

Question

the monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 mi and in June it cost her $460 to drive 800 mi.

Answer 1

Let's assume that a linear function of the form

d = km + b

can be made to describe both months, where d is the cost in the month, m the number of miles driven, and k and b are constants to be found.

Then,

380 = 480k + b
460 = 800k + b

Subtract one equation from the other and we get

80 = 320k
k = 1/4

From this we can determine that b = 260.

Thus your linear function is

d = (m/4) + 260

Of course, Helmut is quite right that the two points don't show that a linear model is the correct one. You can put a whole sihtload of curves through those two points, many circles even.

Answer 2

A linear function easiest you can derive with only two data points. That doesn't necessarily mean that it is a suitable model. Any number of functions with two constants can be made to fit the data.

Answer 3

maybe the cost of the driving car redused