1. Given the directed line segment $P Q$ with the coordinates of the starting point $P$ and the end point $Q$ being $(-1,1)$ and $(2,2)$ respectively, if the line $l: x+m y$ $+m=0$ intersects the extension of $P Q$, then the range of values for $m$ is $\qquad$
$$
\left(-3,-\frac{2}{3}\right)
$$
1. 【Analysis and Solution】The equation of line $l$ is $x+m y+m=0$, which can be rewritten as $x+m(y+1)=0$. This is clearly the equation of a line passing through point $M(0,-1)$. Draw a line $l_{1} / / P Q$ through point $M$, obviously, the slope of $l_{1}$ is $k_{1}=\frac{2-1}{2+1}=\frac{1}{3}$. Draw a line $l_{2}$ through $M$ and $Q$, then the slope of $l_{2}$ is $k_{2}=\frac{3}{2}$. As shown in the figure, the line $l$ intersecting the extension of $P Q$ should be between $l_{1}$ and $l_{2}$, i.e., $k_{1}-m>\frac{2}{3},-3<m<-\frac{2}{3}$.