Question

Assume that $y$ varies inversely as $x$. If $y=7$ when $x=-3,$ how do you find $y$ when $x=7?$

Answer 1

Solve for the required value:

Given that,

• $y$ varies inversely as $x$$\Rightarrow y\propto \frac{1}{x}$
• $y=7$ when $x=-3,$

$y\propto \frac{1}{x}\Rightarrow y=\frac{k}{x}$; where $k$ is a constant

$y=7$ when $x=-3$

$\Rightarrow$$7=\frac{k}{-3}$

$\Rightarrow$$k=7\times \left(-3\right)=-21$

Now, when $x=7$

$\Rightarrow y=\frac{-21}{7}\left[\because y=\frac{k}{x}\right]$

$\Rightarrow$$y=-3$

Hence, the required value is $-3$.