Video: Determining Which Ordered Pairs Satisfy a Given Linear Function

Which set of ordered pairs would make the data in the table represent the function 𝑦 = 2π‘₯? [A] (7, 14), (10, 20) [B] (7, 14), (10, 12) [C] (9, 27), (10, 30) [D] (7, 9), (10, 12) [E] (5, 7), (11, 22)

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Video Transcript

Which set of ordered pairs would make the data in the table represent the function 𝑦 equals two π‘₯?

So we have an input row, where five, blank, blank, and 12 as well as an output row of 10, blank, blank, and 24. So this table represents the function 𝑦 equals two π‘₯. And with 𝑦 equals two π‘₯, π‘₯ is the input, the number that we would plug in, and 𝑦 would be the output, the answer that we would get.

So essentially, we take the input and multiply it by two and we get the output. So with an input of five, five times two gives us 10. And then over here with 12, 12 times two gives us 24. So again, the π‘₯-values are the inputs and the 𝑦-values are the outputs.

So looking at our options for an answer, we need to look at the π‘₯- and 𝑦-values β€” π‘₯ being the inputs 𝑦 being the outputs β€” and seeing which set works with 𝑦 equals two π‘₯. So here, we’ve highlighted the π‘₯-values β€” the inputs β€” in yellow and the output β€” the 𝑦-values β€” in pink. So we will go through each one and see if it satisfies this equation.

We will begin with seven and 14. Is 14 equal to two times seven? It is. And is 20 equal to two times 10? And it is. So, so far, it seems like option A is the correct answer. But let’s double-check every single option to be safe.

For option B, is 14 equal to two times seven? It is. And is 12 equal to two times 10? It is not. So B is not an option.

For option C, we have 27 equals two times nine and 30 equals two times 10. Those are not correct. The 𝑦-values are actually three times as large as the π‘₯-values. So option C would actually represent 𝑦 equals three times π‘₯. And again, it is still not the answer.

Option D is not the answer because nine is not equal to two times seven and 12 is not equal to two times 10. For option D, the 𝑦-values are actually two greater than π‘₯. So we would just need to add two to the π‘₯-values to get the 𝑦-values, again not our answer.

For option E, seven is not equal to two times five; it’s equal to two plus five. And 22 is actually equal to two times 11. So only one of these ordered pairs works. But we need both of them to work. So E is not the answer.

So we had the ordered pair of seven and 14 and the ordered pair of 10 and 20. This satisfied the function 𝑦 equals two π‘₯. So once again, the ordered pairs would be seven, 14 and 10, 20.

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