Determine If Mouse Hovers Over A Drawn Line?

I'm creating a type of drawing program. The user can draw a line, much like in word or paint, etc. But once the line is drawn (to a picturebox or bitmap in memory), I want the user to be able to click on the line and drag it around (translate it).

If I know the coordinates of the endpoints of the line, as well as the pen width it was drawn with, how can I tell if a certain coordinate (mouse location) is contained by the line?

My first thought was to take a mathematical approach, like get an equation for a line, and check to see if the coordinate belonged to it. But for a higher pen width, the line is thicker, and thus contains more points.

How can I tell what coordinates are part of the line? Is there some sort of intersect function in the gdi that takes a line?