6. Given that $x, y$ satisfy
$$
\left\{\begin{array}{l}
x+3 y-3 \leqslant 0, \\
x \geqslant 0, \\
y \geqslant 0 .
\end{array}\right.
$$

Then the range of $z=\frac{y+2}{x-1}$ is ( ).
(A) $[-2,1]$
(B) $(-\infty,-2] \cup[1,+\infty)$
(C) $[-1,2]$
(D) $(-\infty,-1] \cup[2,+\infty)$
6. B.

From the problem, we know that the system of inequalities represents the shaded area in Figure 3.
$$
z=\frac{y+2}{x-1} \text { can be seen as the slope of the line connecting point }(x, y) \text { and point } A(1,-2) \text { }
$$

It is easy to see that,
$$
k_{A O}=-2, k_{A B}=1 .
$$

Therefore, the range of $z$ is
$$
(-\infty,-2] \cup[1,+\infty) \text {. }
$$