Inverse Variations explained.

welcome to moomoomath today we're going to look at inverse variation that is when y varies inversely with x okay here's our example if y is 3 when x is 6 what is k well first of all we need to know an equation okay 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 1 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 a fraction so it's kind of like a proportion with a variable on each end okay then we're going to solve for a k by plugging in our x and our y and multiplying y times x or x times y and then we're going to take that k and plug it back into the original equation y equals k x with y and x being the generic variables and we're going to plug in this k we're going to solve for so let's actually walk through this example okay if y is equal to 3 when x is 6 what is k let's first write our equation down y equals k over x now if y is 3 i'll plug in 3 for y when x is 6 and i'm going to plug in 6 for x and i'm going to leave k as our unknown because we don't know what k is i'm going to stick a 1 underneath my 3 because that's a whole number and whole number always has a 1 then i'm going to do a cross multiplication or cross product 3 times 6 is 18 k times 1 is just k so our value for k is 18. now let's go back and plug it into the original equation leaving x and y as variables and just plugging k in so my final equation is y equals 18 over x and that's how you would write the inverse equation for that problem hope this was helpful