intersect.js

  var intersect = function(a1, a2, b1, b2) {
    var ua_t = (b2.x - b1.x) * (a1.y - b1.y) - (b2.y - b1.y) * (a1.x - b1.x);
    var ub_t = (a2.x - a1.x) * (a1.y - b1.y) - (a2.y - a1.y) * (a1.x - b1.x);
    var u_b  = (b2.y - b1.y) * (a2.x - a1.x) - (b2.x - b1.x) * (a2.y - a1.y);
    if ( u_b != 0 ) {
      var ua = ua_t / u_b;
      var ub = ub_t / u_b;
      if ( 0 <= ua && ua <= 1 && 0 <= ub && ub <= 1 ) {
        return {
          x: a1.x + ua * (a2.x - a1.x),
          y: a1.y + ua * (a2.y - a1.y)
        };
      } else {
        throw "No Intersection";
      }
    } else {
      if ( ua_t == 0 || ub_t == 0 ) {
        throw "Coincident";
      } else {
        throw "Parallel";
      }
    }
  };

It seems you could benefit from a higher level of abstraction. Something along the lines of

var a = Line.through(a1, a2);
var b = Line.through(b1, b2);

if (!a.isParrallelTo(b)) {
  point = a.intersectWith(b);
}