|
Question 1210483: graph 3x=y
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 3 * x
# Generate x values
x_values = np.linspace(-5, 5, 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='$y = 3x$')
# Highlight the origin (y-intercept)
plt.plot(0, 0, 'ro', label='y-intercept (0, 0)')
# Add labels and title
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.title('Graph of $3x = y$')
# Set grid and aspect ratio
plt.axhline(0, color='black', linewidth=0.5)
plt.axvline(0, color='black', linewidth=0.5)
plt.grid(True, linestyle='--', alpha=0.6)
plt.gca().set_aspect('equal', adjustable='box')
# Add legend
plt.legend()
# Save the plot
plt.savefig('graph_3x_equals_y.png')
print("graph_3x_equals_y.png")
```
```text?code_stdout&code_event_index=2
graph_3x_equals_y.png
```
[image-tag: code-generated-image-0-1764864301049337471]
The equation $3x = y$ can be written in slope-intercept form as **$y = 3x + 0$**.
This means the line has:
* A **y-intercept** of $0$, passing through the origin $(\mathbf{0, 0})$.
* A **slope** of $\mathbf{3}$ (or $\frac{3}{1}$), meaning for every $1$ unit you move to the right on the $x$-axis, you move $3$ units up on the $y$-axis.
The graph below shows the line $y = 3x$.
To plot this line, you can use the following points:
* $(0, 0)$ (the y-intercept)
* $(1, 3)$ (using the slope: $x=0+1$, $y=0+3$)
* $(-1, -3)$ (using the slope: $x=0-1$, $y=0-3$)
|
|
|
| |
