Inverse Variation

Today we are going to look at inverse variation. That is when Y varies inversely with X OK here is our example. If Y is three and X is six, what is K? Well first of all we need to know an equation. So here are the rules that go along with inverse variation. Y is equal to K over X and notice inverse, if I stuck a one underneath this Y I would have the Y on the top of the fraction and X on the bottom.so our variables are one on top and one on bottom of our fraction. So it’s kind of like a portion with a variable on each end and then we solve for K by plugging in our X and Y and multiplying our Y times X and X times Y and then we will take that K and plug it into the original equation. Y equals KX with Y and X being the generic variables and we will plug the K that we are going to solve for. Let’s walk through this example. If Y is equal to three and X is six what is K? First, let’s write our equation down. Y equals K over X If Y is three, I’ll plug in three for Y and X is six then I’m plug in six for X and I will leave K as our unknown because we don’t know what K is. Place a one under three because that is a whole number, and a whole number always has a one. Next I’m going to do a cross multiplication or cross product. Three times six is eighteen times one is just K so the value for K is eighteen. Now let’s go back and plug it into the original equation leaving X and Y as variables and just plugging K in. My final equation is Y equals eighteen over X and that’s how you would write the inverse for that problem. Hope this helps.