Answer
a) The required value is $k=96$.
b) The resulting equation is $y=\frac{96}{x}$.
c) The required value is $y=32$
Work Step by Step
(a)
As provided
$y=\frac{k}{x}$
$x=8\ \text{ and }\ y=12$
Put value of $x$ and $y$ in the provided function
$\begin{align}
& y=\frac{k}{x} \\
& 12=\frac{k}{8} \\
& k=96
\end{align}$
Therefore, the value of k is $96$.
b)
Now, put the value of k in $y=\frac{k}{x}$.
So,
$y=\frac{96}{x}$
Therefore, the resulting equation is $y=\frac{96}{x}$.
c)
Putting the value of $x=3$ in $y=\frac{k}{x}$ , we get,
$\begin{align}
& y=\frac{96}{x} \\
& y=\frac{96}{3} \\
& y=32
\end{align}$
Hence, $y=32$ when $x=3$.
