For mathematicians..out there....Calc question...please help me!?

Question

here is the question....

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $454 to drive 480 mi and in June it cost her $580 to drive 900 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) = $

(b) Use part (a) to predict the cost of driving 1900 miles per month.

$

C.What does the slope represent?

a)the cost in dollars per mile

b)the fixed cost (amount she pays even if she does not drive)

C)the cost (in dollars) of driving

d)the distance (in miles) traveled

D. What does the y-intercept represent?

a)the fixed cost (amount she pays even if she does not drive)

b)the distance (in miles) traveled

c)the cost in dollars per mile

d)the cost (in dollars) of driving

Answer 1

A) Let x be the number of miles driven, and let y be the cost.

The slope of the line is rise / run = (580 - 454) / (900 - 480) = 126/420 = 0.3

Then you need to use the point-slope form of the equation for a line to find the

y-intercept.

(y - 454) = 0.3 * (x - 480)

y = 0.3x - 160 + 454

y = 0.3x + 294

So the cost function is (substituting d for x, and C for y)

C(d) = 0.3d + 294.

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B) C(1900) = 0.3*1900 + 294 = $864

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C) The slope represents the cost in dollars per mile.

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D) The y-intercept represents the fixed cost paid even if she doesn't drive.