Math Problem Statement
Graph the equation. y=4x+3
Solution
import numpy as np import matplotlib.pyplot as plt
Define the equation y = 4x + 3
x = np.linspace(-10, 10, 400) # x values range y = 4 * x + 3 # calculate y values
Plot the equation
plt.figure(figsize=(8, 6)) plt.plot(x, y, label="y = 4x + 3", linewidth=2) plt.axhline(0, color='black', linewidth=0.8) # x-axis plt.axvline(0, color='black', linewidth=0.8) # y-axis plt.title("Graph of y = 4x + 3") plt.xlabel("x") plt.ylabel("y") plt.grid(True, linestyle='--', alpha=0.7) plt.legend() plt.show() <<ImageDisplayed>>successHere is the graph of the equation . Let me know if you need further analysis or additional details.
Follow-Up Questions:
- Would you like to know how to find the slope and y-intercept from this equation?
- Do you need help plotting a similar linear equation?
- Would you like to calculate specific points on this line for given x-values?
- Are you interested in comparing this graph to another linear equation?
- Would you like an explanation of what the slope and intercept represent graphically?
Tip: The slope () determines the steepness of the line, and the y-intercept () shows where the line crosses the y-axis.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing in Coordinate Geometry
Formulas
Slope-intercept form y = mx + b
Theorems
Linear equation properties
Suitable Grade Level
Grades 6-8