# How do you use linear equation in business?

In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each $.25 increase in fare.

Given the description above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), find the slope of the graph, find the price at which there will be no more riders, and find the maximum number of riders possible. The vertical axis is the number of riders per day, and the horizontal axis is the fare.

Graph:

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What is the slope of the graph?

The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?

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If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus?

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3) It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour.

a) How far have you traveled after 3 hours?

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b) How far have you traveled after 4 hours?

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c) How far have you traveled after t hours? i.e. write a linear function that expresses the distance traveled, d, as a function of time, t.

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d) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled 3 hours?

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e) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled 4 hours?

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f) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled t hours? i.e. write a linear function that expresses the distance to be traveled to reach St. Louis, s, as a function of time, t.

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#### Solution Preview

Please see the attached file.

Here are the assumptions:

1. There can not be negative number of riders.

2. The bus company does not pay the riders.

These two assumptions have the following impact on the function ...

#### Solution Summary

The 5 pages long solution demonstrates how to use linear equations and apply the slope-intecept data.