Answer
$m=-\dfrac{1}{3}$
Work Step by Step
Using $m=\dfrac{y_1-y_2}{x_1-x_2}$ or the Slope Formula, the slope of the line through $(
-3,1
)$ and $(
3,-1
)$ is
\begin{array}{l}\require{cancel}
m=\dfrac{1-(-1)}{-3-3}
\\\\
m=\dfrac{1+1}{-3-3}
\\\\
m=\dfrac{2}{-6}
\\\\
m=\dfrac{\cancel{2}}{\cancel{2}(-3)}
\\\\
m=-\dfrac{1}{3}
.\end{array}