# If y=-6.3 when x=2/3, how do you find y when x=8 given that y varies inversely as x?

Jun 6, 2017

$y = - \frac{21}{40}$

#### Explanation:

Given that $\text{ "y=kxx1/x" }$ where $k$ is the constant of variation.

Known condition:

$y \text{ "=" "kxx1/x" "->" "-6 3/10" "=" } k \times \frac{1}{\frac{2}{3}}$

$\text{ "->" "-63/10" "=" } k \times \frac{3}{2}$

Multiply both sides by $\frac{2}{3}$

$\text{ "->" "-63/10xx2/3" "=" } k \times 1$

But 2 will divide exactly into 10 by 5 and 3 will divide exactly into 63 by 21 giving:

$\text{ "->" "-(cancel(63)^(21))/(cancel(10)^5)xx(cancel(2)^1)/(cancel(3)^1)" "=" } k$

So $k = - \frac{21}{5}$

Thus we have:$\text{ "y=-21/5xx 1/x" "->" } y = - \frac{21}{5 x}$
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Let $x = 8$ giving:

$y = - \frac{21}{5 \times 8} = - \frac{21}{40}$