Answer
The graph is shown below.
Work Step by Step
$xy=-9$
Divide x on both sides: $xy=-9$,
$\begin{align}
& \frac{xy}{x}=\frac{-9}{x} \\
& y=-\frac{9}{x}
\end{align}$
Now substitute $x=-4$ into the equation $y=-\frac{9}{x}$,
$\begin{align}
& y=\frac{-9}{-4} \\
& =\frac{9}{4} \\
& =2.25
\end{align}$
Now substitute $x=-3$ into the equation $y=-\frac{9}{x}$,
$\begin{align}
& y=\frac{-9}{-3} \\
& =\frac{9}{3} \\
& =3
\end{align}$
Now substitute $x=-2$ into the equation $y=-\frac{9}{x}$,
$\begin{align}
& y=\frac{-9}{-2} \\
& =\frac{9}{2} \\
& =4.5
\end{align}$
Now substitute $x=-1$ into the equation $y=-\frac{9}{x}$,
$\begin{align}
& y=\frac{-9}{-1} \\
& =\frac{9}{1} \\
& =9
\end{align}$
Now substitute $x=1$ into the equation $y=-\frac{9}{x}$,
$\begin{align}
& y=-\frac{9}{1} \\
& =-9
\end{align}$
Now substitute $x=2$ into the equation $y=-\frac{9}{x}$,
$\begin{align}
& y=-\frac{9}{2} \\
& =-4.5
\end{align}$
Now substitute $x=3$ into the equation $y=-\frac{9}{x}$,
$\begin{align}
& y=-\frac{9}{3} \\
& =-3
\end{align}$
Now substitute $x=4$ into the equation $y=-\frac{9}{x}$,
$\begin{align}
& y=-\frac{9}{4} \\
& =-2.25
\end{align}$
Thus, the required table is,
$\begin{matrix}
x & -4 & -3 & -2 & -1 & 1 & 2 & 3 & 4 \\
y=-\frac{9}{x} & 2.25 & 3 & 4.5 & 9 & -9 & -4.5 & -3 & -2.25 \\
\end{matrix}$
Now plot the points and draw two curves.
