Answer
The graph is shown below.
Work Step by Step
$xy=8$
Divide x on both sides $xy=8$,
$\begin{align}
& \frac{xy}{x}=\frac{8}{x} \\
& y=\frac{8}{x}
\end{align}$
Now substitute $x=-4$ into the equation $y=\frac{8}{x}$,
$\begin{align}
& y=\frac{8}{-4} \\
& =-\frac{8}{4} \\
& =-2
\end{align}$
Now substitute $x=-3$ into the equation $y=\frac{8}{x}$,
$\begin{align}
& y=\frac{8}{-3} \\
& =-\frac{8}{3} \\
& =-2.667
\end{align}$
Now substitute $x=-2$ into the equation $y=\frac{8}{x}$,
$\begin{align}
& y=\frac{8}{-2} \\
& =-\frac{8}{2} \\
& =-4
\end{align}$
Now substitute $x=-1$ into the equation $y=\frac{8}{x}$,
$\begin{align}
& y=\frac{8}{-1} \\
& =-\frac{8}{1} \\
& =-8
\end{align}$
Now substitute $x=1$ into the equation $y=\frac{8}{x}$,
$\begin{align}
& y=\frac{8}{1} \\
& =8
\end{align}$
Now substitute $x=2$ into the equation $y=\frac{8}{x}$,
$\begin{align}
& y=\frac{8}{2} \\
& =4
\end{align}$
Now substitute $x=3$ into the equation $y=\frac{8}{x}$,
$\begin{align}
& y=\frac{8}{3} \\
& =2.667
\end{align}$
Now substitute $x=4$ into the equation $y=\frac{8}{x}$,
$\begin{align}
& y=\frac{8}{4} \\
& =2
\end{align}$
Thus, the required table is,
$\begin{matrix}
x & -4 & -3 & -2 & -1 & 1 & 2 & 3 & 4 \\
y=\frac{8}{x} & -2 & -2.667 & -4 & -8 & 8 & 4 & 2.667 & 2 \\
\end{matrix}$
Now plot the points and draw two curves.
