## Real World Applications – Algebra I

### Topic

How do you know which cell phone plan is the cheapest?

### Student Exploration

The student will investigate, compare and determine which cell phone plan is the least expensive over time.

The Task:

- Search for two different cell phone companies (i.e. AT&T, Verizon, Sprint, T-Mobile, Boost, Metro PCS).
- The most organized way to list the cost of each cell phone plan is to make a table. Make a table for each cell phone company. The input \begin{align*}(x)\end{align*} values should be the # of months you have the phone, and the output \begin{align*}(y)\end{align*} values should be the total cost. “Month 0” should be the initial cost of purchasing the cell phone itself.
- Create a graph for each table of points. What are realistic values of \begin{align*}x\end{align*} and \begin{align*}y\end{align*} on this graph? Why?
- Create an equation for each cell phone plan represented in slope-intercept form.
- In each equation, what is the slope? What does this represent in the cell phone plan? What is the \begin{align*}y-\end{align*}intercept in each equation? What does this represent in the cell phone plan? Justify your thinking.
- Which cell phone plan is the cheapest, and for how long?
- When are both cell phone plans the same cost? Use the Substitution Method to solve this system of linear equations you created. What do “\begin{align*}x\end{align*}” and “\begin{align*}y\end{align*}” each represent in this solution?