Inverse Variation Question 3 with Solution Last week, I went over inverse variation, and I gave you four inverse variation problems to try on your own. You can see that post here: Inverse Variation Today I would like to give a solution to the third of those four problems. You can see a solution to the first two problems here: Q1 Q2 Example: If x ≠ 0 and x is directly proportional to y, which of the following is inversely proportional to 1/y2 ? A) x2 B) x C) 1/x D) 1/x2 Try to solve the problem yourself before checking the solution below. Solution: Since x is directly proportional to y, x = ky for some constant k. Taking the reciprocal of each side of this equation gives us 1/x = 1/ky. Cross multiplying yields ky = x. So k = x(1/y). Squaring each side of this last equation gives k2 = x2(1/y2). Since k2 is a constant, x2 is inversely proportional to 1/y2. So the answer is choice A. More Problems with Explanations If you are preparing for the SAT, ACT, or an SAT math subject test, you may want to take a look at the Get 800 collection of test prep books. And if you liked this article, please share it with your Facebook friends: Comments comments