Determine the value of $y$ so that the line segment with endpoints $P(3, y)$ and $Q(-3, -1)$ is parallel to the line segment with endpoints $R(-4, 9)$ and $S(5,6)$.
I began by finding the slope of the second segment: $$\frac{6-9}{5-(-4)}=\frac{-3}{-9}$$ I don't what to do from here, or if I'm supposed to do this.
Hint 1: What you computed is part of what you need, but you should attack the problem by asking: "What is a mathematical formulation of the problem?"
You should then think, "I know two lines are parallel if and only if their slopes are equal (or both undefined)."
So if you compute the slopes $m_1$ and $m_2$ of the lines containing these segments, and equate them, you will have a statement that formulates the problem.
With luck, this will be an equation you can solve for the unknown quantity $y$.
Hint 2: The slope of $RS$ is $-1/3$. The slope of $PQ$ is $(y+1)/6$.
Hint 3: Set the slopes from the previous hint equal to each other and solve for $y$ (which is what the problem asks you to find).