7. In the Cartesian coordinate system, there are two points $P(-1,1)$ $Q(2,2)$, and the graph of the linear function $y=k x-1$ intersects the extension of line segment $P Q$ (the intersection point does not include $Q$). Then the range of the real number $k$ is $\qquad$.
7. $\frac{1}{3}2$'s solution $\Leftrightarrow\left(k-\frac{1}{3}\right) x=\frac{7}{3}$ has a solution $x>2$
$$
\begin{array}{l}
\Leftrightarrow k-\frac{1}{3}>0, \text { and }-\frac{\frac{7}{3}}{k-\frac{1}{3}}>2 \\
\Leftrightarrow \frac{1}{3}<k<\frac{3}{2} .
\end{array}
$$