Using Graphical and Algebraic Approaches for Finding Unknowns of Linear Functions

4.5.5 Using Graphical and Algebraic Approaches for Finding Unknowns of Linear Functions

4.5.5 • Using Graphical and Algebraic Approaches for Finding Unknowns of Linear Functions

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The college student who is looking for a data plan for her cell phone found a third option, which also offers a 2-gigabyte monthly allowance for data.

The monthly cost of this option can be represented by function $C$ , defined by $C (x) = 30 x + 5$ , where $x$ is the gigabytes of data used over the monthly allowance.

Find $C (0.7)$ and explain what it means in this situation.

Compare your answers:

$C (0.7) = 26$ because $30 (0.7) + 5 = 26$ . Your answers may vary, but here is a possible explanation: It means that the cost would be $26 if she used 0.7 gigabyte over the 2-gigabytes allowance in a month.

Her budget is still $50 a month. To find out how many gigabytes of data she could use if she chose this plan, she writes $C (x) = 50$ and solves for $x$ . What value of $x$ makes this equation true? Be prepared to show your reasoning.

Compare your answers:

$x = 1.5$ . Your answers may vary, but here is a possible explanation: Because $C (x) = 30 x + 5$ , we can write $C (x) = 50$ as $30 x + 5 = 50$ and solve for $x$ , which gives 1.5.