Answer
(a.) $k=96$.
(b.) $y=\frac{96}{x}$.
(c.) $y=32$.
Work Step by Step
$\Rightarrow y=\frac{k}{x}$
Substitute $x=8$ and $y=12$.
$\Rightarrow 12=\frac{k}{8}$
Multiply both sides by $8$.
$\Rightarrow 8\cdot12=8\cdot \left (\frac{k}{8}\right )$
Simplify.
$\Rightarrow 96=k$
Hence, the value of $k$ is $96$.
(b.) Substitute $k=96$ into the equation.
$\Rightarrow y=\frac{96}{x}$
Hence, the resulting equation is $y=\frac{96}{x}$.
(c.) Substitute $x=3$ into the equation from part (b.).
$\Rightarrow y=\frac{96}{3}$
Simplify.
$\Rightarrow y=32$
Hence, the value of $y$ is $32$.
