import matplotlib.pyplot as plt import numpy as np

Define the function y = 5x + 2

x = np.linspace(-10, 10, 100) # Generate 100 points from -10 to 10 y = 5 * x + 2

Plot the function

plt.figure(figsize=(8, 6)) plt.plot(x, y, label="y = 5x + 2", linewidth=2)

Add grid, labels, and title

plt.axhline(0, color='black', linewidth=0.8, linestyle="--") # x-axis plt.axvline(0, color='black', linewidth=0.8, linestyle="--") # y-axis plt.title("Graph of y = 5x + 2") plt.xlabel("x") plt.ylabel("y") plt.grid(color='gray', linestyle='--', linewidth=0.5) plt.legend() plt.show() <<ImageDisplayed>>successHere is the graph of the function $y = 5x + 2$. The line has a slope of 5 and a y-intercept at $(0, 2)$.

Would you like assistance analyzing the graph or further questions?

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Here are five related questions:

1. How does the slope $5$ affect the steepness of the line?
2. What happens to the graph if you change the equation to $y = 5x - 2$?
3. Can you find the x-intercept of the line $y = 5x + 2$?
4. How would the graph change if the slope were negative, such as $y = -5x + 2$?
5. What is the significance of the y-intercept in the context of a linear equation?

Tip: The slope in a linear equation determines the steepness and direction of the line, while the y-intercept shows where the line crosses the y-axis.