Math Problem Statement
Graph the function rule. y=5x+2
Solution
import matplotlib.pyplot as plt import numpy as np
Define the function y = 5x + 2
x = np.linspace(-10, 10, 100) # Generate 100 points from -10 to 10 y = 5 * x + 2
Plot the function
plt.figure(figsize=(8, 6)) plt.plot(x, y, label="y = 5x + 2", linewidth=2)
Add grid, labels, and title
plt.axhline(0, color='black', linewidth=0.8, linestyle="--") # x-axis plt.axvline(0, color='black', linewidth=0.8, linestyle="--") # y-axis plt.title("Graph of y = 5x + 2") plt.xlabel("x") plt.ylabel("y") plt.grid(color='gray', linestyle='--', linewidth=0.5) plt.legend() plt.show() <<ImageDisplayed>>successHere is the graph of the function . The line has a slope of 5 and a y-intercept at .
Would you like assistance analyzing the graph or further questions?
Here are five related questions:
- How does the slope affect the steepness of the line?
- What happens to the graph if you change the equation to ?
- Can you find the x-intercept of the line ?
- How would the graph change if the slope were negative, such as ?
- What is the significance of the y-intercept in the context of a linear equation?
Tip: The slope in a linear equation determines the steepness and direction of the line, while the y-intercept shows where the line crosses the y-axis.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Graphing
Formulas
y = mx + b (Slope-Intercept Form)
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 8-10