input: Write a python function to perform linear regression on a given set of input points and plot the result using matplotlib.
  ```python
  assert perform_linear_regression([(-5.2, 2.3), (3.1, 4.9), (2.4, 0.3), (-2.4, -3.2)]) is None
  assert perform_linear_regression([(1, 2), (2, 3), (3, 5)]) is None
  assert perform_linear_regression([(0, 0), (1, 1), (2, 2), (3, 3)]) is None
output: import numpy as np
  import matplotlib.pyplot as plt
  
  def perform_linear_regression(points):
      x = np.array([p[0] for p in points])
      y = np.array([p[1] for p in points])
      
      A = np.vstack([x, np.ones(len(x))]).T
      m, c = np.linalg.lstsq(A, y, rcond=None)[0]
      
      plt.scatter(x, y, color='blue', label='Data Points')
      plt.plot(x, m*x + c, color='red', label='Fitted Line')
      
      plt.xlabel('x')
      plt.ylabel('y')
      plt.legend()
      plt.show()