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Video: Writing the Rule of an Input-Output Table as an Equation

Kathryn Kingham

In this function machine, we put 𝑥 in and get 𝑦 out. Which of these equations describes the rule? [A] 𝑦 = 𝑥 + 5 [B] 𝑦 = 𝑥 + 8 [C] 𝑦 = 𝑥 × 5 [D] 𝑦 = 𝑥 × 8 [E] 𝑦 = 𝑥 − 5.

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Video Transcript

In this function machine, we put 𝑥 in and get 𝑦 out. Which of these equations describes the rule? 𝑦 equals 𝑥 plus five, 𝑦 equals 𝑥 plus eight, 𝑦 equals 𝑥 times five, 𝑦 equals 𝑥 times eight, or 𝑦 equals 𝑥 minus five.

This function table has given us a very important clue. In this function machine or in this function table, you multiply 𝑥 by five and that gives you 𝑦. For example, if we have an 𝑥-value of two, we multiply two times five and that gives us our 𝑦-value of 10.

We are looking for an equation that says 𝑦 equals 𝑥 times five. Only one of the answer choices — only one of the equations — describes the rule correctly 𝑦 equals 𝑥 times five.