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Linear Functions

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Challenge

Linear Functions (discover)
A cell phone company starts the year with a certain number of customers. Each month the company gains or loses the same number of subscribers. This relationship is shown as an equation, a graph, and a table. Using the equation, adjust the coefficient of x to change the number of subscribers that are gained or lost each month and adjust the constant term to change the number of customers the company starts with at the beginning of the year. Notice that the graph of the equation is a straight line. Notice that the table shows the number of subscribers changes by the same amount each month. This constant rate of change means that the equation is a linear function. The graph of a linear function is always a straight line.

Related Concepts

Linear Functions, Mean, Median, Mode, Scatter Plot, Slope of a Line

Fun Facts

Cell phone companies offer many plans with different amounts of included minutes and messages, different base prices, and different costs for going over the number of included minutes and messages. Companies carefully design their plans to earn the most amount of money, not necessarily the most number of customers. To do this, they analyze data from cell phone users and calculate averages to find a single value that is typical for different groups of customers. They also use linear functions to represent the relationships between the base price, included minutes, and overage rate to help decide how to set the amounts for each plan.