'cause 2 divided by 1/2 is 4 so here we are scaling up Y so they are going to do the opposite things they vary inverse, and you could try it with the negative way of it as well so here we are multiplying by 2 and once again it is not always neatly written for you like this it could be rearranged in a bunch different ways but it will still be inverse variation as long as they are algebraically equivalent so you could multiply both side of this equation right here by X and you would get XY is equal to 2, this is also inverse variation you would get this exact same table over here you could divide both sides of this equation by Y and you could X is equal to 2/Y which is also the same thing as 2 times 1/Y so notice Y varies inversely with X and you could just manipulate this algebraically to show that X varies inversely with Y so Y varies inversely with X this is the same thing (as seen in this example) as saying that X varies inveresely with Y and there is other things we could take this and divide both sides by 2 and you would get Y/2 is equal to 1/X there's all sort of crazy things so in general if you see an expression that relates two variables and they say do they vary inversely or directly or maybe neither you could either try to make a table like this if you scale up X by certain amount and Y gets scaled up by the same amount that is direct variation if you scale up X, you may want to try it a couple of different times and you scale down Y, do the opposite with Y, then it is probably inverse variation a sure way to know what you're dealing with it's to actually algebraically manipulate the equation so it gets back to either this form that tells you it's inverse variation or this form, which will tell you that it is direct variation