How to align, enlarge and center the following contents?

1. No vertical rule, no double rules.
2. No m type, one can use w{c}.
3. Use a local macro in order to ease inputting the coordinates.
4. Add some vertical space between the points.
5. Increase the value of \jot in order to increase the distance between rows in aligned.
6. Add some vertical space below the middle rule and above the bottom rule.

\documentclass{article}
\usepackage{amsmath}
\usepackage{array,booktabs}

\begin{document}

\begin{center}
\begin{tabular}{
  @{}
  w{c}{0.33333\columnwidth}
  @{}
  w{c}{0.33333\columnwidth}
  @{}
  w{c}{0.33333\columnwidth}
  @{}
}
\toprule
A pair of points & Slope & Type \\
\midrule
\addlinespace
$\setlength{\arraycolsep}{0pt}
\newcommand{\point}[3]{#1&(&#2&,{}&#3&)}
\begin{array}{ r r r l r r }
  \point{A}{2}{-3} \\[2ex]
  \point{B}{-1}{4}
\end{array}$
& 
$\addtolength{\jot}{6pt}\begin{aligned}
m   &= \frac{y_B-y_A}{x_B-x_A}\\
    &= \frac{4-(-3)}{-1-2}\\
    &= -\frac{7}{3}
\end{aligned}$
&
Decreasing \\
\addlinespace
\bottomrule
\end{tabular}
\end{center}

\end{document}

A approach that uses stackengine in the left column, and eliminates the m columns to achieve vertical centering. Also \addstackgap was used to add vertical buffer above/below the middle column.

\documentclass[preview,varwidth,border=12pt]{standalone}
\usepackage[a5paper,margin=5mm]{geometry}
\usepackage{amsmath}
\usepackage{tabstackengine}
\TABstackMath
\setstackgap{L}{1.2\normalbaselineskip}
\renewcommand{\arraystretch}{1.5}
\begin{document}
\begingroup\tabcolsep=30pt
\begin{tabular}{|c|c|c|}\hline
A pair of points & Slope & Type \tabularnewline\hline\hline
\Matrixstack[r]{
A(&2,& -3)\\
B(&-1,& 4)
} & 
\addstackgap[5pt]{$
\begin{aligned}
m   &= \frac{y_B-y_A}{x_B-x_A}\\[4pt]
    &= \frac{4-(-3)}{-1-2}\\[4pt]
    &= -\frac{7}{3}
\end{aligned}$}
 & Decreasing \tabularnewline\hline
\end{tabular}\endgroup
\end{document}

Here's a way with cellspace, in the place of \arraystretch, and \multirow:

\documentclass[preview,varwidth,border=12pt]{standalone}
\usepackage[a5paper, margin=5mm]{geometry}
\usepackage{mathtools}
\usepackage{array}
\usepackage{cellspace}
\setlength{\cellspacetoplimit}{4pt}
\setlength{\cellspacebottomlimit}{4pt}
\newcolumntype{M}[1]{S{m{#1}}}
\usepackage{multirow}

\begin{document}

\begin{tabular}{|wc{0.3\linewidth}| >{\centering}M{0.3\linewidth}|wc{0.2\linewidth}|}\hline
A pair of points & Slope & Type \tabularnewline\hline\hline
\multirow{3.9}{=}{\centering$\begin{matrix}
A (\phantom{-}2,-3)\\
B(-1,\phantom{-}4)
\end{matrix}$} &
$ \begin{aligned}
m &= \frac{y_B-y_A}{x_B-x_A}\\
    &= \frac{4-(-3)}{-1-2}\\
    &= -\frac{7}{3}
\end{aligned} $ & 
\multirow{4}{=}{\centering Decreasing} \tabularnewline\hline
\end{tabular}

\end{document}