Answer
The graph is shown below.
Work Step by Step
$xy=-2$
Divide x on both sides: $xy=-2$,
$\begin{align}
& \frac{xy}{x}=\frac{-2}{x} \\
& y=-\frac{2}{x}
\end{align}$
Now substitute $x=-4$ into the equation $y=-\frac{2}{x}$,
$\begin{align}
& y=\frac{-2}{-4} \\
& =0.5
\end{align}$
Now substitute $x=-3$ into the equation $y=-\frac{2}{x}$,
$\begin{align}
& y=\frac{-2}{-3} \\
& =\frac{2}{3} \\
& =0.667
\end{align}$
Now substitute $x=-2$ into the equation $y=-\frac{2}{x}$,
$\begin{align}
& y=\frac{-2}{-2} \\
& =\frac{2}{2} \\
& =1
\end{align}$
Now substitute $x=-1$ into the equation $y=-\frac{2}{x}$,
$\begin{align}
& y=\frac{-2}{-1} \\
& =\frac{2}{1} \\
& =2
\end{align}$
Now substitute $x=1$ into the equation $y=-\frac{2}{x}$,
$\begin{align}
& y=-\frac{2}{1} \\
& =-2
\end{align}$
Now substitute $x=2$ into the equation $y=-\frac{2}{x}$,
$\begin{align}
& y=-\frac{2}{2} \\
& =-1
\end{align}$
Now substitute $x=3$ into the equation $y=-\frac{2}{x}$,
$\begin{align}
& y=-\frac{2}{3} \\
& =-0.667
\end{align}$
Now substitute $x=4$ into the equation $y=-\frac{2}{x}$,
$\begin{align}
& y=-\frac{2}{4} \\
& =-0.5
\end{align}$
Thus, the required table is,
$\begin{matrix}
x & -4 & -3 & -2 & -1 & 1 & 2 & 3 & 4 \\
y=-\frac{2}{x} & 0.5 & 0.667 & 1 & 2 & -2 & -1 & -0.667 & -0.5 \\
\end{matrix}$
Now plot the points and draw two curves.
