import numpy as np import matplotlib.pyplot as plt

Define the line equation: y + 1 = (1/3)(x + 9)

x = np.linspace(-20, 20, 400) y = (1/3) * (x + 9) - 1

Plot the line

plt.figure(figsize=(8, 6)) plt.plot(x, y, label=r"$y+1=\frac{1}{3}(x+9)$") 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.title("Graph of the Line") plt.xlabel("x-axis") plt.ylabel("y-axis") plt.legend() plt.show() <<ImageDisplayed>>successHere is the graph of the line $y + 1 = \frac{1}{3}(x + 9)$. Do you need further details or have any questions?

1. How do the slope and intercept affect the graph?
2. What is the domain and range of this line?
3. Can you explain the role of transformations in this equation?
4. How do vertical and horizontal shifts apply here?
5. What is the slope-intercept form of this equation?

Tip: For quick graphing, always rewrite the equation in the form $y = mx + b$.