# If y varies inversely as the square of x and y = 8 when x = 2, then what is the value of y when x = -1?

Apr 15, 2016

The answer is $32$, based on an inverse proportionality model.

#### Explanation:

According to the statement,

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

This expression takes us to the exact formula:

$y = \frac{\alpha}{x} ^ 2$

where $\alpha$ is a constant of proportionality. To find it, we need a numerical value: $y \left(x = 2\right) = 8$. By substituting:

$8 = \frac{\alpha}{2} ^ 2 \rightarrow \alpha = 32$

So our formula is:

$y = \frac{32}{x} ^ 2$

Now, let us calculate $y \left(x = - 1\right)$:

$y = \frac{32}{- 1} ^ 2 = 32$