SOLUTION: y-8=-x

Question 1210482: y-8=-x
Answer by CPhill(2138) (Show Source): You can put this solution on YOUR website!
```python?code_reference&code_event_index=2
import matplotlib.pyplot as plt
import numpy as np
# Define the function
def line_function(x):
return -x + 8
# Generate x values
x_values = np.linspace(-5, 10, 400)
# Generate y values
y_values = line_function(x_values)
# Create the plot
plt.figure(figsize=(8, 6))
plt.plot(x_values, y_values, label='$y = -x + 8$')
# Highlight the intercepts
plt.plot(0, 8, 'ro', label='y-intercept (0, 8)')
plt.plot(8, 0, 'go', label='x-intercept (8, 0)')
# Add labels and title
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.title('Graph of $y - 8 = -x$')
# Set grid and axes
plt.axhline(0, color='black', linewidth=0.5)
plt.axvline(0, color='black', linewidth=0.5)
plt.grid(True, linestyle='--', alpha=0.6)
# Set limits to clearly show the intercepts
plt.xlim(-2, 10)
plt.ylim(-2, 10)
# Add legend
plt.legend()
# Save the plot
plt.savefig('graph_y_minus_8_equals_minus_x.png')
print("graph_y_minus_8_equals_minus_x.png")
```
```text?code_stdout&code_event_index=2
graph_y_minus_8_equals_minus_x.png
```
[image-tag: code-generated-image-0-1764864400960668627]
The equation $y - 8 = -x$ can be easily graphed by rewriting it in the **slope-intercept form** ($y = mx + b$).
$$y = -x + 8$$
This line has the following key properties:
* **Slope ($m$):** $\mathbf{-1}$ (or $\frac{-1}{1}$), meaning for every $1$ unit you move right, you move $1$ unit down.
* **Y-intercept ($b$):** $\mathbf{8}$, meaning the line crosses the $y$-axis at the point $(\mathbf{0, 8})$.
* **X-intercept:** $\mathbf{8}$, meaning the line crosses the $x$-axis at the point $(\mathbf{8, 0})$.
The graph below shows the line $y = -x + 8$.
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