I need to know whether or not two line segments intersect. I thought the formula for that is $y = mx + b$, but I don't think that will work for what I need; at least, I think I need to first know whether the line segments intersect, because that formula just gives the point where the two lines will eventually intersect.
For example, say I have two line segments. Line $1$ has a starting point of $(15, 10)$ and its ending point is $(30, 17)$. Line $2$ has a starting point of $(29,5)$ and an ending point of $(33, 14)$. These shouldn't intersect within those coordinates, but, by using $y = mx + b$, I find that they approximately intersect at $(35, 19.5)$.
How can I find out whether these line segments happen to intersect each other?