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.

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:
http://www.mathsisfun.com/equation_of_line.html

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:
http://www.mathsisfun.com/y_intercept.html

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: http://www.mathsisfun.com/gradient.html

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.

great--thanks!

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.