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Linear Functions with Spreadsheets

By

Tonya DeGeorge

 


The spreadsheet can be used with a variety of mathematical explorations.  For example, suppose you were studying linear functions and you wanted your students to investigate the relationship between the total amount of money they will make and the number of weeks:

 

Sara currently has $70 in her savings account and wants to start saving her money for a used car that is worth about $2000. She makes $130 every week babysitting for her neighbor and plans to put the full amount in her bank account.  How many weeks will it take her to save the $2000 needed for her car?

 

To begin, we would have to set up a table in excel (as shown below).  First, we will have to take note that Sara currently has $70 in her bank account.  So at zero weeks, she has $70.  Every week she adds in the $130 into her savings account.  So at week #1, she has (70 + 130), or $2000.  This table is shown in the picture below (taken from excel).  If you would like to use excel, please click here. (Only the first 20 weeks are shown).

 

 

 

Students should be able to visually see the linear pattern that is occuring in the table and possibly generate the following equation: , where t represents the total amount of money in Sara's savings account and w represents the number of weeks. From the table, students should be able to see that it will take about 15 weeks for Sara to accumulate enough money for her car – that is, if she doesn’t spend any money!

 

However, excel can also provide some graphical features which may be nice to display to students. For instance, in the same given problem we can set up a linear graph.  (Once you highlight the y-values (in this case, the column that represents the total amount of money in Sara’s bank account) and go to the gallery function, you can select your line graph.)

 

 

From the chart, students can clearly see why the function is called “linear.”  From here students can investigate other types of functions (quadratic, exponential, etc.) using excel and generating graphs.

 


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