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.)

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

[tex]\frac{y - 11400}{11400 - 7800} = \frac{x - 20000}{20000 - 10000}[/tex]

⇒ [tex]\frac{y - 11400}{3600} = \frac{x - 20000}{10000}[/tex]

⇒ [tex]y - 11400 = \frac{9}{25}(x - 20000)[/tex]

⇒ [tex]y - 11400 = \frac{9}{25}x - 7200[/tex]

⇒ [tex]y = \frac{9}{25}x + 4200[/tex]

⇒ 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)