Video Transcript
For the following table, find the algebraic equation that shows the proportional relationship between ๐ฅ and ๐ฆ.
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 ๐ฆ equals ๐๐ฅ, where ๐ is the constant rate that is changing the variables. And we can use the formula ๐ฆ equals ๐๐ฅ to help us figure out what the constant rate of change in this table is.
Weโre asking here, what is happening to ๐ฅ to give us ๐ฆ? What weโre multiplying our ๐ฅ by to give ๐ฆ? And our first instance: ๐ฅ equals six and ๐ฆ 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.
Letโs check the other two points in our table to make sure thatโs 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 isnโt 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 ๐ฆ equals two times ๐ฅ.
