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 $y=\frac{2}{x}$,
$\begin{align}
& y=\frac{2}{-4} \\
& =-\frac{2}{4} \\
& =-0.5
\end{align}$
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 $y=\frac{2}{x}$,
$\begin{align}
& y=\frac{2}{4} \\
& =0.5
\end{align}$
Hence, 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.
