numpy as np import matplotlib.pyplot as plt

Define the function y = -1/4x + 5

def f(x): return (-1/4) * x + 5

Generate values for x and calculate corresponding y values

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

Plot the graph

plt.figure(figsize=(8,6)) plt.plot(x_values, y_values, label=r'$y = -\frac{1}{4}x + 5$', color='blue')

Add labels and title

plt.title(r"Graph of $y = -\frac{1}{4}x + 5$") plt.xlabel("x") plt.ylabel("y")

Add a grid for better visualization

plt.grid(True)

Add a legend

plt.legend()

Show the plot

plt.axhline(0, color='black',linewidth=1) plt.axvline(0, color='black',linewidth=1) plt.show()Here's the graph of the equation $y = -\frac{1}{4}x + 5$. It's a straight line with a slope of $-\frac{1}{4}$ and a y-intercept at $y = 5$.

Do you need more details on how the graph is constructed or the meaning of the slope and intercept?

Here are 5 related questions you might find useful:

1. What does the slope represent in the equation $y = -\frac{1}{4}x + 5$?
2. How would the graph change if the slope were positive instead of negative?
3. What happens to the graph if the y-intercept were different?
4. How do you calculate the slope between two points on this line?
5. What does the graph look like when $x = 0$?

Tip: A negative slope means the line decreases as $x$ increases, which is the case here with $-\frac{1}{4}$.