# Y varies inversely with twice the value of x. When y = 8, x = 2. How do you find y when x = 8?

Mar 28, 2016

$y = 2 \text{ at } x = 8$

#### Explanation:

$y = k \times \frac{1}{2 x}$

$\text{so } 2 x y = k$

Given that when $y = 8 \text{, } x = 2$ so we have:

$2 \left(2\right) \left(8\right) = k$

$\implies k = 32$

So our equation becomes:

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

This is the same as:

$y = \frac{32}{2} \times \frac{1}{x}$

so $y = \frac{16}{x}$
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So when $x = 8$

$\textcolor{b r o w n}{y = \frac{16}{x}} \textcolor{b l u e}{\text{ " ->" } y = \frac{16}{8} = 2}$