You can use coefficients of linear fit to make a legend like in this example:
import seaborn as sns
import matplotlib.pyplot as plt
from scipy import stats
tips = sns.load_dataset("tips")
# get coeffs of linear fit
slope, intercept, r_value, p_value, std_err = stats.linregress(tips['total_bill'],tips['tip'])
# use line_kws to set line label for legend
ax = sns.regplot(x="total_bill", y="tip", data=tips, color="b",
line_kws={'label':"y={0:.1f}x+{1:.1f}".format(slope,intercept)})
# plot legend
ax.legend()
plt.show()
If you use more complex fitting function you can use latex notification: https://matplotlib.org/users/usetex.html