Answer
$m(x)=\begin{cases}
1,\text{ if }0\leq x<3\\
-\dfrac{1}{3}\text{ if }x\geq 3
\end{cases}$
Work Step by Step
The graph consists of two lines. We determine the slope of each of them.
For the line corresponding to $x\in[0,3)$ we choose two points and determine the slope $m_1$:
$(0,1),(2,3)$
$m_1=\dfrac{3-1}{2-0}=1$
For the line corresponding to $x\in[3,\infty)$ we choose two points and determine the slope $m_2$:
$(3,2),(6,1)$
$m_2=\dfrac{1-2}{6-3}=-\dfrac{1}{3}$
The slope function $m(x)$ can be written:
$m(x)=\begin{cases}
1,\text{ if }0\leq x<3\\
-\dfrac{1}{3}\text{ if }x\geq 3
\end{cases}$
