# 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.