Answer
The linear function whose graph contains the points $\left( 6,11 \right)$ and $\left( -6,-11 \right)$ is $y=\frac{11}{6}x$.
Work Step by Step
First calculate the slope:
Substitute $-11$ for ${{y}_{2}}$, $11$ for ${{y}_{1}}$, $-6$ for ${{x}_{2}}$ and $6$ for ${{x}_{1}}$ in $m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$,
$\begin{align}
& m=\frac{-11-11}{-6-6} \\
& =\frac{-22}{-12} \\
& =\frac{11}{6}
\end{align}$
Substitute $6$ for ${{x}_{1}}$, $11$ for ${{y}_{1}}$ and $\frac{11}{6}$ for $m$.
$\begin{align}
& y-11=\frac{11}{6}\left( x-6 \right) \\
& y-11=\frac{11}{6}x-11
\end{align}$
$y=\frac{11}{6}x$
