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(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)= ?

Update:

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

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  • 2 months ago
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    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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