1. Inversely/Directly proportional SAT problem

If x cannot equal zero and x is inversely proportional to y, which of the following is directly proportional to 1/x^2?

A: -1/y^2
B: 1/y^2
C: 1/y
D: y
E: y^2

I can't seem to get my head around this problem, usually I'm pretty good at these but I just can't put this one together. I would appreciate any help, thanks.

2. Originally Posted by bk brains
If x cannot equal zero and x is inversely proportional to y, which of the following is directly proportional to 1/x^2?

A: -1/y^2
B: 1/y^2
C: 1/y
D: y
E: y^2

I can't seem to get my head around this problem, usually I'm pretty good at these but I just can't put this one together. I would appreciate any help, thanks.
$\displaystyle x=\frac{1}{y}$

Therefore, the problem should now look like this

$\displaystyle \frac{1}{(\frac{1}{y})^2}$

Which is the same as

$\displaystyle \frac{1}{\frac{1^2}{y^2}}$

Which is the same as

$\displaystyle \frac{1}{1}$ Divided by $\displaystyle \frac{1}{y^2}$

Which is the same as

$\displaystyle \frac{1}{1}$ multiplied by $\displaystyle \frac{y^2}{1}$

Therefore, the solution is

$\displaystyle y^2$

I reversed a step while typing; therefore, I have corrected my answer sorry for the confusion