Line $l_1$ has equation $2x+y=5$ and goes through $A=(3,-1)$. Line $l_2$ has equation $y=3$ and meets line $l_1$ at point $B$. Line $l_3$ has positive slope, goes through point $A$, and meets $l_2$ at point $C$. The area of $△ABC$ is $8$. What is the slope of $l_3$?