One more update

problem.py

import unittest

def find_slope(x1,y1,x2,y2):
    slope = (y2 - y1) / (x2 - x1)
    return slope

def find_intercept(x,y,slope):
    intercept = y - slope * x
    return intercept

# NOTE: runs in O(N^3) time

def solution(point_list):
     point_list = [ (float(x),float(y)) for (x,y) in point_list ]
     point_list = list(set(point_list)) # remove duplicates
     line_list = []
     for i in range(0, len(point_list)):
         for j in range(i+1, len(point_list)):
             for k in range(j+1, len(point_list)):
                 if i !=j and i!=k and j!=k:
                     (x1 , y1 ) = point_list[i]
                     (x2 , y2 ) = point_list[j]
                     (x3 , y3 ) = point_list[k]
                     #http://mathworld.wolfram.com/Collinear.html
                     if x1*(y2-y3)+x2*(y3-y1)+x3*(y1-y2)==0.0:
                         #collinear!
                         try:
                             vector = find_slope(x1,y1,x2,y2)
                             point = (0.0,find_intercept(x1,y1,vector))     
                         except ZeroDivisionError:
                             vector = "UND"
                             point = (x1,0.0)  
                         line = {'vector':vector, 'point':point}
                         line_list.append(line)
     # remove duplicate lines
     line_list=[dict(t) for t in set([tuple(d.items()) for d in line_list])]
     return line_list     

class Test(unittest.TestCase):
    def test_solution_2(self):
        problem_instance = [(0, 0), (1, 1), (3, 4), (2, 2)]
        expected = [
            {'point': (0.0, 0.0), 'vector': 1.0}
        ]
        returned = solution(problem_instance)
        self.assertEqual(expected,returned)

    def test_solution_a(self):
        problem_instance = [(0, 0), (1, 1), (3, 4), (2, 2),(4,5),(5,6)]
        expected = [
            {'point': (0.0, 0.0), 'vector': 1.0}, 
            {'point': (0.0, 1.0), 'vector': 1.0}
        ]
        returned = solution(problem_instance)
        self.assertEqual(expected,returned)


    def test_solution_2_empty_sol(self):
        problem_instance = [(0, 0), (0, 0), (0,0)]
        expected = []
        returned = solution(problem_instance)
        self.assertEqual(expected,returned)
        problem_instance = [(0, 0), (1,1), (1,1)]
        expected = []
        returned = solution(problem_instance)
        self.assertEqual(expected,returned)

    def test_solution_2_undefined(self):
        problem_instance = [(0, 0), (0, 1), (0,2)]
        expected = [{'point': (0.0, 0.0), 'vector': 'UND'}]
        returned = solution(problem_instance)
        self.assertEqual(expected,returned)


if __name__ == "__main__":
    unittest.main()