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Video: Writing a Linear Function in a Real-World Context

Kathryn Kingham

Ruby spends $3.88 every day on transportation to and from work. Write a function rule that relates the total amount of money Ruby spends on transportation to the number of Ruby’s working days. Let 𝑥 represent the number of working days and 𝑦 the total amount of money she spends on transportation.

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Video Transcript

Ruby spends three dollars and eighty-eight cents every day on transportation to and from work. Write a function rule that relates the total amount of money Ruby spends on transportation to the number of Ruby’s working days. Let 𝑥 represent the number of working days and 𝑦 the total amount of money she spends on transportation.

We need to write a function rule. Our function rule will have an 𝑥 that represents the number of working days and a 𝑦 that represents the total amount of money Ruby spends on transportation. We can think of our function rule like a machine; you input some information that you know, the function rule occurs, and then it gives you some kind of output.

In our case, we’ll input the number of working days; these are the days that Ruby uses the transportation. After the function rule occurs in our machine, it will output the total amount spent on transportation for those working days. The question is what happens here. What happens inside the function rule in our problem? How do we go from the working days to the total money spent? And this is the key. The key is the three dollars and eighty-eight cents Ruby spends on her working days.

Our function rule is the number of working days multiplied by three dollars and eighty-eight cents and that gives us the total that Ruby spent. Our problem wants us to use 𝑥 to represent the number of working days and 𝑦 to represent the total amount of money. So we substitute 𝑥 and 𝑦, respectively, for the working days and the total amount. Simplifying it a little bit, three dollars and eighty-eight cents times 𝑥 equals 𝑦. Using this function rule, we’ll always be able to find out the total amount of money that Ruby spends on transportation if we know 𝑥 — how many days she worked.