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Applications of Linear Graphs

Linear equations in word problems

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Finding the Cheapest Cell Phone Plan
Teacher Contributed

Real World Applications – Algebra I


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:

  1. Search for two different cell phone companies (i.e. AT&T, Verizon, Sprint, T-Mobile, Boost, Metro PCS).
  2. 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.
  3. 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?
  4. Create an equation for each cell phone plan represented in slope-intercept form.
  5. 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.
  6. Which cell phone plan is the cheapest, and for how long?
  7. 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?

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