Answer
$-\dfrac{5}{13}$
Work Step by Step
With the given points, $\left(
\dfrac{3}{2}, -\dfrac{1}{2}
\right)$ and $\left(
-\dfrac{2}{3},\dfrac{1}{3}
\right)$, then
\begin{array}{l}\require{cancel}
y_1=
-\dfrac{1}{2}
,\\y_2=
\dfrac{1}{3}
,\\x_1=
\dfrac{3}{2}
,\text{ and }\\ x_2=
-\dfrac{2}{3}
.\end{array}
Using $m=\dfrac{y_1-y_2}{x_1-x_2}$ or the Slope Formula, the slope, $m,$ of the line is
\begin{array}{l}\require{cancel}
m=\dfrac{-\dfrac{1}{2}-\dfrac{1}{3}}{\dfrac{3}{2}-\left(-\dfrac{2}{3}\right)}
\\\\
m=\dfrac{-\dfrac{1}{2}-\dfrac{1}{3}}{\dfrac{3}{2}+\dfrac{2}{3}}
\\\\
m=\dfrac{-\dfrac{3}{6}-\dfrac{2}{6}}{\dfrac{9}{6}+\dfrac{4}{6}}
\\\\
m=\dfrac{-\dfrac{5}{6}}{\dfrac{13}{6}}
\\\\
m=\dfrac{-\dfrac{5}{\cancel6}}{\dfrac{13}{\cancel6}}
\\\\
m=-\dfrac{5}{13}
.\end{array}
Hence, the slope, $m,$ is $
-\dfrac{5}{13}
$.
