Line $l\_1$ has equation $3 x-2 y=1$ and goes through $A=(-1,-2)$. Line $l\_2$ has equation $y=1$ 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 $\triangle A B C$ is $3$ . What is the slope of $l\_3$? (2013 AMC 12B Problems, Question \#8) 
选项为:A:$$\frac23$$  B:$$\frac34$$  C:$$1$$  D:$$\frac43$$  E:$$\frac32$$  请回答其中一个选项.