How to change the color of a single line plot based on another variable

I want to plot a line using the following equation.

y = x(1+0.25ε)
Where,
x = {0, 1, 2, ..., 200}
ε = np.random.randn()

And i want to change the color of the plot based on slop. I.e it should be blue when the slope is positive and it should be red when slope is negative. Like the following

import numpy as np

N = 100  # Change the number of data points to 100
x = np.array([i for i in range(N)])  # Use x=[i for i in range(100)]
epsilon = np.random.rand(N)  # Generate random noise for N data points
y = x * (1 + 0.25 * epsilon)  # Calculate y with noise
slope = np.gradient(y, x)  # Calculate the slope of y with respect to x

# Separate the data points based on the condition (slope > 0)
positive_slope = slope > 0
x_positive_slope = x[positive_slope]
y_positive_slope = y[positive_slope]

# Separate the data points based on the condition (slope < 0)
negative_slope = slope < 0
x_negative_slope = x[negative_slope]
y_negative_slope = y[negative_slope]

plt.figure(figsize=(10, 4))
plt.plot(x_positive_slope, y_positive_slope, color='r', label='Positive Slope')
plt.plot(x_negative_slope, y_negative_slope, color='b', label='Negative Slope')
plt.legend()
plt.xlabel('x')
plt.ylabel('y')
plt.title('Line Plot with Color Trend Following Slope')
plt.grid(True)
plt.show()

but it plots two different lines. Any idea ?

Note that plt.plot works with points, while you want to color the line segments which connect these points. As such, your call plt.plot(x_positive_slope, y_positive_slope, ...) simply connects all starting points of line segments with positive slope.

You can apply the "multicolored line" approach from the tutorial. It converts the continuous curve into short segments, and colors each segment via a colormap.

import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
import numpy as np

x = np.arange(51)
ε = np.random.randn(x.size)
y = x * (1 + 0.25 * ε)
segments = np.c_[x[:-1], y[:-1], x[1:], y[1:]].reshape(-1, 2, 2)
slope = np.diff(y)
lc = LineCollection(segments, cmap='RdYlBu')
lc.set_array(slope > 0)
fig, ax = plt.subplots()
ax.add_collection(lc)
ax.set_xlim(x.min(), x.max())
ax.set_ylim(y.min(), y.max())
plt.show()

import numpy as np
import matplotlib.pyplot as plt

N = 100  # Change the number of data points to 100
x = np.arange(N)  
epsilon = np.random.rand(N)  # Generate random noise for N data points
y = x * (1 + 0.25 * epsilon)  # Calculate y with noise
slope = np.diff(y)  # Calculate the slope of y with respect to x

negative = slope < 0
positive = ~negative

xx = np.array([x[:-1], x[1:]])
yy = np.array([y[:-1], y[1:]])

xp = xx[:, positive]
yp = yy[:, positive]

xn = xx[:, negative]
yn = yy[:, negative]

plt.figure(figsize=(10, 4))
first_positive_line, *_ = plt.plot(xp, yp, c='b')
first_negative_line, *_ = plt.plot(xn, yn, c='r')

plt.legend([first_positive_line, first_negative_line], 
           ['Positive Slope', 'Negative Slope'])

plt.xlabel('x')
plt.ylabel('y')
plt.title('Line Plot with Color Trend Following Slope')
plt.grid(True)
plt.show()