Question

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.)

Answer 1

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)