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The yearly cost y for driving a certain car is $7,800 for 10,000 miles

and $11,400 for 20,000 miles. Let x be the number of miles driven

in a year

Write a linear function that models this data. Then use the function to find the given value.



y=

(Simplify your answer and round to TWO decimal places, including zeros as needed. Example: 2 should be written as 2.00. Do not include commas.)



Estimate the number of miles driven when the yearly cost is $9,636.00.

____ miles

(Round your answer to TWO decimal places, including zeros as needed.

Example: 2 should be written as 2.00. Do not include commas.)

User Defuz
by
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1 Answer

6 votes

Answer:

y = 0.36x + 4200.00

15100.00 miles.

Explanation:

If the yearly cost for driving x miles is given by y dollars then the two ordered pairs to find the linear relation between x and y are (10000,7800) and (20000,11400).

So, the equation will be


(y - 11400)/(11400 - 7800) = (x - 20000)/(20000 - 10000)


(y - 11400)/(3600) = (x - 20000)/(10000)


y - 11400 = (9)/(25)(x - 20000)


y - 11400 = (9)/(25)x - 7200


y = (9)/(25)x + 4200

y = 0.36x + 4200.00 ........... (1) (Answer)

Now, for y = $9636.00, from equation (1),

9636 = 0.36x + 4200

⇒ 0.36x = 5436

x = 15100.00 miles. (Answer)

User Ramz
by
6.7k points