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.
$
x=\frac{1}{y}
$

Therefore, the problem should now look like this

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

Which is the same as

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

Which is the same as

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

Which is the same as

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

Therefore, the solution is

$
y^2$

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