Q:

Table and graph do not align

The table and graph are not vertically aligned and I don't know how to fix it. Any suggestions?
\begin{tabular}{|c|c|} \hline
    $x$     &   $y$ \\ \hline 
    $-2$    &   $-5$    \\ \hline
    $-1$    &   $-3$    \\ \hline
    $0$ &   $-1$    \\ \hline
    $1$ &   $1$ \\ \hline
    $2$ &   $3$ \\ \hline
    $3$ &   $5$ \\ \hline
\end{tabular} 
\hspace{5cm}
\begin{tikzpicture}[scale=.3]
    \begin{scope}
        \clip (-10,-20) rectangle (10,0);
        \draw[step=2cm,gray,very thin]
            (-12,-22) grid (10,0);
    \end{scope} 
    \draw [<->] (-11,-10) -- (11,-10);
    \draw [<->](0,-21) -- (0,1);
    \clip (-10,-20) rectangle (10,0);
\end{tikzpicture}

A:

You can use the t option for tabular and (current bounding box.base) for baseline= in the tikzpicture:
\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tabular}[t]{|c|c|} \hline
    $x$     &   $y$ \\ \hline 
    $-2$    &   $-5$    \\ \hline
    $-1$    &   $-3$    \\ \hline
    $0$ &   $-1$    \\ \hline
    $1$ &   $1$ \\ \hline
    $2$ &   $3$ \\ \hline
    $3$ &   $5$ \\ \hline
\end{tabular}% 
\hspace{5cm}%
\begin{tikzpicture}[baseline=(current bounding box.base),scale=.3]
    \begin{scope}
        \clip (-10,-20) rectangle (10,0);
        \draw[step=2cm,gray,very thin]
            (-12,-22) grid (10,0);
    \end{scope} 
    \draw [<->] (-11,-10) -- (11,-10);
    \draw [<->](0,-21) -- (0,1);
    \clip (-10,-20) rectangle (10,0);
\end{tikzpicture}

\end{document}

Notice the character % that I added twice to remove spurious blank spaces. Perhaps instead of a hardwired horizontal space you could use \hfill.

