Answer
The graph is shown below
Work Step by Step
$xy=-6$
Divide x on both sides of the equation $xy=-6$,
$\begin{align}
& \frac{xy}{x}=\frac{-6}{x} \\
& y=-\frac{6}{x}
\end{align}$
Now substitute $x=-4$ into the equation $y=-\frac{6}{x}$,
$\begin{align}
& y=\frac{-6}{-4} \\
& =\frac{6}{4} \\
& =\frac{3}{2}
\end{align}$
Now substitute $x=-3$ into the equation $y=-\frac{6}{x}$,
$\begin{align}
& y=\frac{-6}{-3} \\
& =\frac{6}{3} \\
& =2
\end{align}$
Now substitute $x=-2$ into the equation $y=-\frac{6}{x}$,
$\begin{align}
& y=\frac{-6}{-2} \\
& =\frac{6}{2} \\
& =3
\end{align}$
Now substitute $x=-1$ into the equation $y=-\frac{6}{x}$,
$\begin{align}
& y=\frac{-6}{-1} \\
& =\frac{6}{1} \\
& =6
\end{align}$
Now substitute $x=1$ into the equation $y=-\frac{6}{x}$,
$\begin{align}
& y=-\frac{6}{1} \\
& =-6
\end{align}$
Now substitute $x=2$ into the equation $y=-\frac{6}{x}$,
$\begin{align}
& y=-\frac{6}{2} \\
& =-3
\end{align}$
Now substitute $x=3$ into the equation $y=-\frac{6}{x}$,
$\begin{align}
& y=-\frac{6}{3} \\
& =-2
\end{align}$
Now substitute $x=4$ into the equation $y=-\frac{6}{x}$,
$\begin{align}
& y=-\frac{6}{4} \\
& =-\frac{3}{2}
\end{align}$
Thus, the required table is,
$\begin{matrix}
x & -4 & -3 & -2 & -1 & 1 & 2 & 3 & 4 \\
y=-\frac{6}{x} & \frac{3}{2} & 2 & 3 & 6 & -6 & -3 & -2 & -\frac{3}{2} \\
\end{matrix}$
Now plot the points and draw two curves.
