Cell Phone Problem
Pay-2-Much Wireless wants its customers to purchase a phone
plan that will generate the most revenue for the company.
Customers want to pick the most economical plan to meet
their needs.
You are a customer-advocate mathematician. Three of your
friends have asked for your help in selecting the best plan for
each of their needs. Below are the three plans that Pay-2Much Wireless provides before tax.
Economy Plan Talker Plan
Chatterbox
Plan
Monthly Service
$20
$40
$100
Charge **
Per Minute Rate
$0.50
$0.20
No Charge
** The Monthly charge does not include any airtime.
Here’s the projected cellular phone airtime use for each of your
friends:
 Your friend Quinterra will need to average 700 minutes of
airtime per month.
 Your friend Yancey will need on average 160 minutes of airtime
per month
 Your friend Ashley will need on average 40 minutes of airtime per
month.
Using the multiple-way (Graphs, numbers, words, and symbols/equations),
recommend which of the three plans your friends should subscribe to. You must
support your recommendations with the mathematical information from your
analysis.
Created by UCLA Department of Math and Teaching – modified by Nicole Kim
Slope
1. What is the definition of rate of change?
2. What is the definition of slope?
3. Fill out the T-Chart for each cell phone plan from the Cell Phone
Problem.
Economy
X(min)
Y ($)
0
1
2
3
4
Talker
X (min)
Y($)
0
1
2
3
4
Chatterbox
X (min) Y ($)
0
1
2
3
4
4. What is the increase of the bill amount in $ per min of each plan?
Economy __________
Talker _________
Chatterbox Plan ______
5. What is the formula to find the slope of two given points on a line
graph?
Nicole Kim - 2014
6. On graph paper, graph the Economy Plan.
7. Find the slope of the line graph representing the Economy Plan by using
a right triangle. Then find the slope by using the slope formula.
8. On the same graph paper, graph the Talker Plan. Make sure to use a
different color for the line graph.
9. Find the slope of the line graph representing the Talker Plan by using a
right triangle. Then find the slope by using the slope formula
10. On the same graph paper, graph the Chatter Box Plan. Make sure to
use a different color for the line graph.
11. Find the slope of the line graph representing the Chatter Box Plan by
using a right triangle. Then find the slope by using the slope formula
12. Compare the slopes of three lines on your graph. Interpret your
results in context of the problem.
Nicole Kim - 2014
Extra Practice
For #1-5, Find the slope of each line. Show your work.
1)
2)
3) A line that passes through the points (-1,3) and (2,0)
4) A line that passes through the points (-4,2) and (2, 6).
5) The line below.
Intercepts
1. What is the definition of Y-intercept?
2. What is the Y-intercept of the Economy Plan? What does this mean in
context of minutes and payment?
3. What is the Y-intercept of the Talker Plan? What does this mean in
context of minutes and payment?
4. What is the Y-intercept of the Chatterbox Plan? What does this mean
in context of minutes and payment?
5. What is the x-intercept of the Talker Plan? Explain the meaning of
the x-intercept in terms of the problem. Does the x-intercept carry
meaning in this context?
Nicole Kim - 2014
Slope –Intercept Form
Complete the steps to derive the equation to solve for y by using the slope formula.
___________________
Multiplication Property of Equality
___________________
Addition Property of Equality
____________________
Slope –Intercept Form
1. What is the slope of the line graph above?
2. What is the y-intercept of the line graph above?
3. In the form y = mx +b, what does m represent?
4. In the form y = mx +b, what does b represent?
Now, look at the graphs of the Cell Phone Project.
5. Write an equation of the line that represents the Economy Plan in slope-intercept form.
6.
Write an equation of the line that represents the Talker Plan in slope-intercept form.
7. Write an equation of the line that represents the Chatter Box Plan in slope-intercept form.