# (a) Find a linear function C that models the cost of driving x miles per month.?

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her driving cost was $380 for 480 mi and in June her cost was $460 for 800 mi. Assume that there is a linear relationship between the monthly cost C of driving a car and the distance x driven.

(a) Find a linear function C that models the cost of driving x miles per month.

C(x)= ?

B.) What is the slope of the line

C.) At what rate does Lynn's cost increase for every additional mile she drives?

$ ? per mile

### 1 Answer

- L. E. GantLv 72 months agoFavorite Answer
linear function:

let y represent dollars

let x represent miles

then y = mx + k for some k

slope = rise/run

rise is change in dollars = 460 - 380 = 80

run is change in miles = 800 - 480 = 320

so slope = 80/320 = 1/4

when y = 380, x = 480

so 380 = 480/4 + k

==> k = 380 - 120 = 260

verify:

when y = 460, x = 800

so 460 = 800/4 + k

==> k = 460 - 200 = 260

So C(x) = (x/4) + 260

increase in cost per mile is 0.25 dollars

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