import numpy as np import matplotlib.pyplot as plt

Define the inequality line: x - y = 2

x = np.linspace(-5, 10, 400) y = x - 2

Set up the plot

plt.figure(figsize=(8, 6))

Plot the boundary line (x - y = 2)

plt.plot(x, y, label="x - y = 2", color="blue")

Fill the region where x - y >= 2

plt.fill_between(x, y, y + 20, where=(y + 20 > y), color="lightblue", alpha=0.5)

Labels and grid

plt.title("Graph of x - y ≥ 2") plt.xlabel("x") plt.ylabel("y") plt.axhline(0, color="black",linewidth=0.5) plt.axvline(0, color="black",linewidth=0.5) plt.grid(color = 'gray', linestyle = '--', linewidth = 0.5) plt.legend() plt.show() <<ImageDisplayed>>successHere is the graph of the linear inequality $x - y \geq 2$. The shaded region represents all points that satisfy the inequality.

Do you want further details about the graph or have any questions?

Here are 5 related questions you might explore:

1. How do we determine the boundary line for a linear inequality?
2. What changes in the graph if the inequality becomes strict ($>$ instead of $\geq$)?
3. How can we test whether a point lies in the solution region?
4. How do we graph systems of linear inequalities?
5. What happens to the graph if we flip the inequality sign?

Tip: Always substitute a test point (like $(0,0)$) into the inequality to verify which region to shade.