Video: Forming an Equation to Describe the Relation between Inputs and Outputs in a Given Table

For the following table, find the algebraic equation that shows the proportional relationship between ๐‘ฅ and ๐‘ฆ.

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Video Transcript

For the following table, find the algebraic equation that shows the proportional relationship between ๐‘ฅ and ๐‘ฆ.

What is that mean โ€” a proportional relationship? The variables in a function will change at a constant rate in a proportional relationship, and we use the formula ๐‘ฆ equals ๐‘˜๐‘ฅ, where ๐‘˜ is the constant rate that is changing the variables. And we can use the formula ๐‘ฆ equals ๐‘˜๐‘ฅ to help us figure out what the constant rate of change in this table is.

Weโ€™re asking here, what is happening to ๐‘ฅ to give us ๐‘ฆ? What weโ€™re multiplying our ๐‘ฅ by to give ๐‘ฆ? And our first instance: ๐‘ฅ equals six and ๐‘ฆ equals 12. How did we go from six to 12? 12 equals ๐‘˜ times six. We recognize that our ๐‘˜, our constant rate of change, is two. Two times six equals 12; our constant rate of change equals two.

Letโ€™s check the other two points in our table to make sure thatโ€™s true for them as well. Does seven times two equal 14? Yes, it does. Does eight times two equal 16? Yes, so all three of our points are following a constant rate of change of two. But our work here isnโ€™t finished. Our question is asking, what is the algebraic equation that shows this? We plug in two to our proportional relationship formula. And then our algebraic equation becomes ๐‘ฆ equals two times ๐‘ฅ.

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