Inverse Variation - Problem 3
If two points vary inversely, that means that the product of the x and y values of the first point is equal to the product of the x and y values of the second point. This is known as the product rule for inverse variation: given two ordered pairs (x1, y1) and (x2, y2), x1y1 = x2y2. Plug the x and y values into the product rule and solve for the unknown value.
Here I'm given two points but one of them has a variable and I'm told they vary inversely and I have to solve for that variable. If the points (1/2,4) and (x,1/10) are solutions to an inverse variation, find x.
Okay well here is what I know about inverse variation. I know that two variables vary inversely if their product is equals to some constant, the product of the x and y values. What that told us is that we have what's called the product rule. If you multiply an x and a y value that are from an ordered pair that go together it's going to be equal to the product of the other ordered pair values. That's called the product rule for inverse variation.
So let's try it we know that x1 and y1 are Â½ and 4 so I'm going to multiply those and that's going to be equal to the product of x and 1/10 from my second pair. All we have to do now is solve for x. Â½ of 4 is equal to 2. 2 is going to be equal to x divided by 10 so to solve for x what I want to do is multiply both sides by 10 and I'm going to have x equals 20.
There's my x value that tells me that if I stuck 20 in there I will get the same product between 1/2 and 4 as I will get between 20 and 1/10. When you come to inverse variation keep this really important formula in your brain. If you can remember that then you can use your logic skills to derive this product rule.
Good luck guys you can do it with inverse variation.