# If y=7, when x=6, how do you find y when x=-21 given that y varies inversely as x?

Mar 19, 2017

$y = \textcolor{g r e e n}{- 2}$

#### Explanation:

If $y$ varies inversely as $x$ then
$\textcolor{w h i t e}{\text{XXX}} x \times y = c$ for some constant $c$

We are told that $\left(x , y\right) = \left(6 , 7\right)$ is a solution to the required relation;
so
$\textcolor{w h i t e}{\text{XXX")6 xx 7 =c color(white)("XX")rarrcolor(white)("XX}} c = 42$

$\textcolor{w h i t e}{\text{XXXXXXXXXXX")rarrcolor(white)("XX}} x \times y = 42$

When $x = - 21$
$\textcolor{w h i t e}{\text{XXX")(-21) xx y = 42color(white)("XX")rarrcolor(white)("XX}} y = - 2$#