How to plot lower boundary with a scatter plot with curve_fit and a linear line function?

Question

I use the following code to plot a scatter plot. I have been trying to plot the lower boundary for it. I tried following the other question but I was unable to replicate it for my objective function and data. The code is as follows :

from numpy import arange
import pandas as pd
from pandas import read_csv
from scipy.optimize import curve_fit
from matplotlib import pyplot
 

def objective(x, a, b):
    return a * x + b
 
events = pd.read_excel('values.xlsx')
x = events.loc[:, 'Value']
y = events.loc[:, 'Frame']

popt, _ = curve_fit(objective, x, y)


a, b = popt
pyplot.scatter(x, y)


x_line = arange(min(x), max(x), 1)
y_line = objective(x_line, a, b)
pyplot.plot(x_line, y_line, '--', color='purple')
xmin, xmax = pyplot.xlim() # the limits of the x-axis for drawing the line
ymin, ymax = pyplot.ylim()

pos_min = np.argmin(x)
pos_max = np.argmax(x)

alpha_min = x[pos_min] 
alpha_max = x[pos_max] 

pyplot.show()

I want to plot the lower boundary of the points like .