Adding an arbitrary line to a matplotlib plot in ipython notebook

You can directly plot the lines you want by feeding the plot command with the corresponding data (boundaries of the segments):

plot([x1, x2], [y1, y2], color='k', linestyle='-', linewidth=2)

(of course you can choose the color, line width, line style, etc.)

From your example:

import numpy as np
import matplotlib.pyplot as plt

np.random.seed(5)
x = np.arange(1, 101)
y = 20 + 3 * x + np.random.normal(0, 60, 100)
plt.plot(x, y, "o")


# draw vertical line from (70,100) to (70, 250)
plt.plot([70, 70], [100, 250], 'k-', lw=2)

# draw diagonal line from (70, 90) to (90, 200)
plt.plot([70, 90], [90, 200], 'k-')

plt.show()

It's not too late for the newcomers.

plt.axvline(x, color='r') # vertical
plt.axhline(x, color='r') # horizontal

It takes the range of y as well, using ymin and ymax.