title: How do you make line segments between two points and find out how many points intersect the line?
body: <p>I have code that generates all the possible lines between points:</p>
  
  <pre><code>import matplotlib.pyplot as plt
  import matplotlib.lines as lines
  import itertools 
  
  fig=plt.figure()
  ax=fig.add_subplot(111)
  all_data = [[1,10],[2,10],[3,10],[4,10],[5,10],[3,1],[3,2],[3,3],[3,4],[3,5]]
  x, y = zip(*all_data)
  plt.scatter(x,y)
  for pair in itertools.combinations(all_data,2):
      line=lines.Line2D(*zip(*pair))
      line.set_color('brown')
      ax.add_line(line)
  
  plt.show()
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/kbe2A.png" alt="enter image description here"></p>
  
  <p>but I want how many points each line intersects. (points are blue)</p>