linear equation set up

elizabethj

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Joined
Jan 29, 2013
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9
Here is the problem I am working on..

Lynn found in May her driving cost was $390 for 760mi and in June her cost was $410 for 800mi. Assume there is a linear relationship between the monthly cost C of driving a car and the distance driven d. Find a linear equation that relates to C and d.

After the equation is written I'll have to graph it and then use it to predict other costs. I can do both of those but only once I figure out how to set up the original equation.

I would like to do as much of the work as possible so if someone could please help me get started or give me some information on how to do this it would be very much appreciated.

Thanks!
 
We want to find the function \(\displaystyle C(d)\). We are given the points \(\displaystyle (d_1,C_1)=(760,390)\) and \(\displaystyle (d_2,C_2)=(800,410)\). The slope of the line will be:

\(\displaystyle m=\dfrac{\Delta C}{\Delta d}=\dfrac{C_2-C_1}{d_2-d_1}\). Once you find this slope, then use the point-slope formula using either of the given points:

\(\displaystyle C-C_n=m(d-d_n)\) where \(\displaystyle n\in\{1,2\}\)

Finally, solve for \(\displaystyle C\), and you will have \(\displaystyle C\) as a function of \(\displaystyle d\):

\(\displaystyle C=m(d-d_n)+C_n\)

At this point, plug in one of your points, and simplify.

Let us know of your progress. :cool:
 
Thank you so much!

I solved for a slope of 1/2

Then used the point slope form and solved for C, which ended up being
C=1/2d+10

Then substituted in 1500mi for d, which made C=760 dollars

So glad I found this website, thank you for your help!
 
Last edited:
Thank you for your feedback...it is gratifying to know that the help given was appreciated and useful. You correctly derived the linear function which you were asked to find. :cool:
 
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