Math CentralQuandaries & Queries


Question from teresa, a student:

Driving a rental car x miles cost y= 0.25x + 25 dollars.

(a) How much would it cost to rent the car but not drive it?
(b) How much does it cost to drive the car 1 additional mile?
(c) What is the y-intercept of y= 0.25x + 25? What does it represent?
(d) What is the slope of y= 0.25x + 25? What does it represent?

Hi Teresa,

Let me look at a similar question. I am wondering how many years I should keep my car before I consider selling it and a dealer told me that an approximate value of my car $y$ is given by

\[y = \$20~000 - \$3~600 x\]

where x is the number of years I have owned that car.

What does this function tell me?

When I bought the car $x = 0$ and then \[y = \$20~000 - \$3~600 \times 0 = \$20~000\] and hence its value then (hopefully what I paid for it) was $\$20 000.$

What was its value one year later? That is when $x = 1$ and hence \[y = \$20~000 - \$3~600 \times 1 = \$20~000 - \$3~600 = \$16~400\] and hence it has dropped $\$3~600$ in value in the first year.

What was its value one year later, that is when $x = 2?$ Looking at the function \[y = \$2~ 000 - \$3~ 600 x\] you can see that it will drop another $\$3 600$ in value.

The slope of the line \[y = \$20~000 - \$3~600 x\] is $-3~600$ and the units are dollars per year and it tells me how much the value of my car decreases every year.

Try your problem now and if you get stuck, write back and tell us what you did and we will try to help,

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