<p>If x =/= 0 and x is inversely proportional to y, which of the following is directly proportional to 1/x2?</p>
<p>I narrowed my answer choices down to:
(B) 1/y^2
(E) y^2</p>
<p>I chose B, which was the wrong answer. Here was my though process:</p>
<p>x = 1/y
y = 1/x
y^2 = 1/x^2</p>
<p>So then I thought, if x gets bigger, then 1/x^2 gets smaller and then y^2 gets smaller. Doesn't that mean that y^2 and 1/x^2 are INVERSELY proportional? So that's why I went with choice B. I know this is wrong. Can someone explain why? Thanks</p>
<p>You can search the forum to find complete explanations for this problem. But your reasoning was almost enough to get to the right answer: You are right that if x gets bigger, both 1/x2 and y2 get smaller – so they vary inversely with x – actually with the square of x, but no matter – but how do they vary WITH EACH OTHER? They are directly proportional. Quick way to see it: make up an x value, find 1/x2 and y2. Then repeat with a new x value. You’ll get new values for 1/x2 and y2. But if you set up ratios (new values over old values) you will see that they are proportional. If you don’t follow this, let me know and I will post specific numbers for you to see…</p>