LINEAR EQUATIONS Introduction To

Systems of Equations

Cell Phone Dilemma

Description

In this activity students will learn to:

1. Make Comparisons.

2. Determine a function rule.

3. Analyze data.

Contents Pages

Student worksheets 2-3

Expected Outcomes

Students will

§ Review Graphing Equations

§ Determine the solution for a system of equations – Using a graph or table

§ Analyze data

NCTM Standards 2000

Algebra Representation

Geometry Communication

Worksheet

Your parents want to reward you for receiving all A’s on your report card. They agree to purchase a cell phone for you, but you must find the best plan. You narrow your search to two plans that include a free phone and the cost per minute.

Cell Phone Company / Phone Plans
No Dropped Calls / $19.95 Monthly Service fee; plus 10 cents per minute
Text Message Today / No Service fee; plus 15 cents per minute

Answer the following questions.

1. How will you solve this problem? Explain the reason you chose that method.

2. If you use 100 minutes, which plan is best? Why is it best?

3. If you use 250 minutes, which plan is best? Why is it best?

4. If you use 500 minutes, which plan is best? Why is it best?

5. How many minutes would you have to use for both plans to be equal?

6. Develop an equation in the slope-intercept form (y=mx+b) for each plan.

7. Using your graphing calculator, graph each equation.

To enter the equations into the graphing calculator follow the directions below.

Press y=

Highlight y1=

Type in the first equation

Press ENTER

In y2= Type in the second equation

Press ENTER

Press ZOOM

Highlight 6:ZStandard

Press ENTER

8. Only the graph of one equation is visible. Explain why. What can you do to have both graphs visible?

9. Using the trace feature or the table set feature of your graphing calculator, check your answers for examples 1-5.

10. Based on your findings, which plan would you choose? Justify your answer.

Teacher Notes and Solutions

1. Answers will vary – possibilities include using a table of values, guess and check, and graphically.

2. Text Message Today. Your bill would be only $15.00 and the bill for No Dropped Calls would be $29.95.

3. Text Message Today. Your bill would be only $37.50 and the bill for No Dropped Calls would be $44.95.

4. No Dropped Calls. Your bill for would be only $69.95 and the bill for Text Message Today would be $75.00.

5. 399 minutes.

6. No Dropped Calls - y = .10x + 19.95

Text Message Today - y = .15x

7. Check students’ calculators.

8. They should see that changing the size of the window would accommodate the graphs.

9. Check their work.

10. Answers will vary. You want them to see that it depends on how many minutes you will use monthly.