# If y varies inversely as x, and y = 12 as x = 2, how do you find y for the x-value of 6?

Jul 9, 2016

$x = 4$

#### Explanation:

As $x$ and $y$ are inversely proportional, the equation can be represented as $x = \frac{k}{y}$.

Substituting $x = 2$ and $y = 12$, we get $2 = \frac{k}{12}$ => $k = 12 \cdot 2$ => $k = 24$.

Equation can be represented as $x = \frac{24}{y}$. So, when $y = 6$, we get $x = \frac{24}{6}$ => $x = 4$

Jul 9, 2016

$y = 4$

#### Explanation:

Write as an inverse proportion first then make an equation by multiplying by k,

$y \propto \frac{1}{x} \text{ " rArr " " y = k/x " } k = x \times y$

Find the value of k.

$k = 2 \times 12 = 24$

$y = \frac{24}{x} \text{ "rArr " } y = \frac{24}{6}$

$y = 4$

You can now find any value of y or x if you are given the x or the y value.