2. For which values of the parameter $a$ is the function $f(x)=a(x+1)+2(x-3)$ increasing, and its graph intersects the y-axis at the coordinate origin?
2. We rewrite the given function as $f(x)=(a+2) x+a-6$. Considering that the function is increasing if $k>0$, it follows that $a+2>0$. The solution is $a>-2$. The function intersects the y-axis below the origin if $f(0)<0$. This implies that $a-6<0$, and the solution is $a<6$. The appropriate solution is $a \in(-2,6)$.

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