Google Answers Logo
View Question
Q: writing equations ( Answered 5 out of 5 stars,   0 Comments )
Subject: writing equations
Category: Science > Math
Asked by: twods-ga
List Price: $20.00
Posted: 14 Jun 2006 23:16 PDT
Expires: 14 Jul 2006 23:16 PDT
Question ID: 738299
write an equation for this story problem:

As the price of a car wash increases by $1.50, 8 fewer people will
visit the car wash.  The "y" intercept is 87.  So at $1.50, 79 people
will go; at $3.00, 71 people; at $4.50, 63 people; at $6.00, 55
people, etc.
Subject: Re: writing equations
Answered By: palitoy-ga on 15 Jun 2006 00:26 PDT
Rated:5 out of 5 stars
Hello twods-ga,

Thank-you for your question.

The easiest way to solve this question is to tabulate the information
and draw a quick graph.  I find it is always easier to visualise the
data when you can see a picture of what is going on!

x      y
0.00   87
1.50   79
3.00   71
4.50   63
6.00   55

If you plot this it is obvious to see that the data produces a
straight line on your graph.

The equation of all straight lines is of the format y = mx + c where m
is the gradient of the slope and c is the intercept of the slope on
the y-axis.  This can be verified here:

If we draw a line through the points on our graph we can see that the
line crosses the y-axis at 87.  This information is also given to us
in the question and the proof of this concept can be seen here:

To work out the gradient of the graph we need to know how many units
the line drops in how many units along the x-axis.  We can do this by
taking 2 data point pairs and finding the difference between the
paired values and then dividing the results.  To see verification of
this you can visit:

Let's take these points:

1.50 & 79
6.00 & 55

The difference between the two y points is 55-79 = -24
The difference between the two x points is 6.00-1.50 = 4.50

Dividing these two results gives us the gradient of the line: -24 /
4.50 = -5.33333333 (or -5 and one third or -5 point 3 recurring).

Putting all this information together... we now know the intercept (c)
on the line is 87, the gradient (m) of the line is -5 1/3 and that an
equation of a straight line is y = mx + c.

The equation is therefore y = -5.333333333x + 87

This equation could also be written as: y = -(16/3)x + 87

You can double-check the solution by inserting some of the known
values of x and y into the equation.

If you require any further assistance on this subject please do not
hesitate to ask for clarification.
twods-ga rated this answer:5 out of 5 stars

I appreciate the links--it helped me understand the "gradiant"--I keep
confusing it with just the numerical difference between points on the
graph--i.e, 1.5 for x and 8 for y.

There are no comments at this time.

Important Disclaimer: Answers and comments provided on Google Answers are general information, and are not intended to substitute for informed professional medical, psychiatric, psychological, tax, legal, investment, accounting, or other professional advice. Google does not endorse, and expressly disclaims liability for any product, manufacturer, distributor, service or service provider mentioned or any opinion expressed in answers or comments. Please read carefully the Google Answers Terms of Service.

If you feel that you have found inappropriate content, please let us know by emailing us at with the question ID listed above. Thank you.
Search Google Answers for
Google Answers  

Google Home - Answers FAQ - Terms of Service - Privacy Policy