Aligned environment effecting tabular environment

Question

I have successfully incorporated an aligned environment in my tabular environment, but now my second column is not aligned with my first. I think that I need to remove the automatic line break after the aligned environment, but do not know how. Is this my problem?

\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,array,calc,tikz}
\begin{document}
\noindent {\bf Determine the average rate of change between the indicated points}\\
\begin{table}[!htbp]
\begin{tabular}{m{3in} m{3in}}
$\begin{aligned}
1. \hspace{1ex} f(x) &= x^2+5x+6\\
&\text{a. From -3 to 0.}\\
&\text{b. From -3 to -2.}\\
&\text{c. From -1 to 2.}
\end{aligned}$ &
2. \raisebox{dimexpr-\height+.7\normalbaselineskip}{
\begin{tikzpicture}[scale=0.25]
\draw[step=1cm,gray,very thin] (-5,-5) grid (5,5);
\draw[<->, ultra thick] (-6,0)--(6,0);
\draw[<->, ultra thick] (0,-6)--(0,6);
\node[below] at (6,0) {$x$};
\node[left] at (0,6) {$y$};
\draw[blue, thick, <->,domain=-1.5:4.5] plot (\x, {2*\x-3});
\end{tikzpicture}}\\
&\\
&\\
\end{tabular}
\end{table}

Answer 1

You can use the [t] option for aligned, the p column type, and a small adjustment with \raisebox so that the top side of the figure be aligned a little higher than the base line:

\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,array,calc,tikz}

\begin{document}

\noindent \textbf{Determine the average rate of change between the indicated points}
\begin{table}[!htbp]\setlength{\fboxsep}{0pt}
\begin{tabular}{p{3in} >{\arraybackslash}p{3in}}
$\begin{aligned}[t]
1. \hspace{1ex} f(x) &= x^2+5x+6\\
&\text{a. From -3 to 0.}\\
&\text{b. From -3 to -2.}\\
&\text{c. From -1 to 2.}
\end{aligned}$ &
2. \raisebox{\dimexpr-\height + 1.5ex}{
\fbox{\begin{tikzpicture}[scale=0.25]
\draw[step=1cm,gray,very thin] (-5,-5) grid (5,5);
\draw[<->, ultra thick] (-6,0)--(6,0);
\draw[<->, ultra thick] (0,-6)--(0,6);
\node[below] at (6,0) {$x$};
\node[left] at (0,6) {$y$};
\draw[blue, thick, <->,domain=-1.5:4.5] plot (\x, {2*\x-3});
\end{tikzpicture}}}
\\
&\\
&\\
\end{tabular}
\end{table}

\end{document}

Answer 2

I don't think that, typographically speaking, it's appropriate to use an aligned environment here. Instead, I believe one should use nested enumerate environments.

\documentclass[12pt]{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,calc,tikz}

\usepackage[shortlabels]{enumitem}
\setlist[enumerate,1]{nosep}
\setlist[enumerate,2]{label=\alph*.,nosep}

\begin{document}

\subsubsection*{Determine the average rate of change between the indicated points}

\noindent
%% place the 1st-level enumerated items in side-by-side 'minipage' environments.
\begin{minipage}{0.5\textwidth}
\begin{enumerate}
\item $f(x) = x^2+5x+6$
  \begin{enumerate}
  \item from $-3$ to $0$
  \item from $-3$ to $-2$
  \item from $-1$ to $2$
  \end{enumerate}
\end{enumerate}
\end{minipage}%
\begin{minipage}{0.5\textwidth}
\begin{enumerate}[2.]
\item \quad \begin{tikzpicture}[scale=0.25, 
      baseline=(current bounding box.center)]
  \draw[step=1cm,gray,very thin] (-5,-5) grid (5,5);
  \draw[<->, ultra thick] (-6,0)--(6,0);
  \draw[<->, ultra thick] (0,-6)--(0,6);
  \node[below] at (6,0) {$x$};
  \node[left] at (0,6) {$y$};
  \draw[blue, thick, <->,domain=-1.5:4.5] plot (\x, {2*\x-3});
  \end{tikzpicture}
\end{enumerate}
\end{minipage}
\end{document}