Answer
The graph is shown below
Work Step by Step
$xy=8$
Divide x on both sides: $xy=4$,
$\begin{align}
& \frac{xy}{x}=\frac{4}{x} \\
& y=\frac{4}{x}
\end{align}$
Now substitute $x=-4$ into the equation $y=\frac{4}{x}$,
$\begin{align}
& y=\frac{4}{-4} \\
& =-\frac{4}{4} \\
& =-1
\end{align}$
Now substitute $x=-3$ into the equation $y=\frac{4}{x}$,
$\begin{align}
& y=\frac{4}{-3} \\
& =-\frac{4}{3} \\
& =-1.33
\end{align}$
Now substitute $x=-2$ into the equation $y=\frac{4}{x}$,
$\begin{align}
& y=\frac{4}{-2} \\
& =-\frac{4}{2} \\
& =-2
\end{align}$
Now substitute $x=-1$ into the equation $y=\frac{4}{x}$,
$\begin{align}
& y=\frac{4}{-1} \\
& =-\frac{4}{1} \\
& =-4
\end{align}$
Now substitute $x=1$ into the equation $y=\frac{4}{x}$,
$\begin{align}
& y=\frac{4}{1} \\
& =4
\end{align}$
Now substitute $x=2$ into the equation $y=\frac{4}{x}$,
$\begin{align}
& y=\frac{4}{2} \\
& =2
\end{align}$
Now substitute $x=3$ into the equation $y=\frac{4}{x}$,
$\begin{align}
& y=\frac{4}{3} \\
& =1.33
\end{align}$
Now substitute $x=4$ into the equation $y=\frac{4}{x}$,
$\begin{align}
& y=\frac{4}{4} \\
& =1
\end{align}$
Thus, the required table is,
$\begin{matrix}
x & -4 & -3 & -2 & -1 & 1 & 2 & 3 & 4 \\
y=\frac{4}{x} & -1 & -1.33 & -2 & -4 & 4 & 2 & 1.33 & 1 \\
\end{matrix}$
Now plot the points and draw two curves.
