import matplotlib.pyplot as plt import numpy as np

Define the function

def f(x): return -x - 6

Generate x values

x_values = np.linspace(-10, 10, 400) y_values = f(x_values)

Plotting the function

plt.figure(figsize=(8, 6)) plt.plot(x_values, y_values, label=r"$y = -x - 6$", linewidth=2) plt.xlabel("x") plt.ylabel("y") plt.title("Graph of $y = -x - 6$") 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 equation $y = -x - 6$. The line has a slope of -1 and a y-intercept at -6, which determines its downward trajectory as x increases.

Would you like more details on interpreting this line or have other questions?

Here are five related questions that might expand your understanding:

1. How do we find the x-intercept of the line $y = -x - 6$?
2. What does changing the slope in $y = mx + b$ affect in the graph?
3. How would the line look if we increased the y-intercept to -2?
4. How do parallel lines relate to this equation?
5. How does graphing inequalities like $y < -x - 6$ differ?

Tip: When graphing, always label the slope and intercepts for easier interpretation.