import numpy as np
import matplotlib.pyplot as plt

A = np.asarray([
  [2, 1],
  [-0.5, 1],
  [-6, 1]
])

b = np.asarray([-1,1,-2])

def line(i, x):
  return (-b[i] + x*A[i,0])/A[i,1]

if __name__ == "__main__":

  x0 = -1
  x1 = 2

  plt.plot([x0, x1], [line(0,x0), line(0,x1)])
  plt.plot([x0, x1], [line(1,x0), line(1,x1)])
  plt.plot([x0, x1], [line(2,x0), line(2,x1)])

  p_hat = np.dot(np.linalg.inv(np.dot(A.T,A)), np.dot(A.T, b))

  plt.scatter(p_hat[0], p_hat[1])
  plt.xlim(-3,3)
  plt.ylim(-3,3)
  plt.gca().set_aspect('equal')
  plt.show()