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 y=5x+2y = 5x + 2. The line has a slope of 5 and a y-intercept at (0,2)(0, 2).

Would you like assistance analyzing the graph or further questions?


Here are five related questions:

  1. How does the slope 55 affect the steepness of the line?
  2. What happens to the graph if you change the equation to y=5x2y = 5x - 2?
  3. Can you find the x-intercept of the line y=5x+2y = 5x + 2?
  4. How would the graph change if the slope were negative, such as y=5x+2y = -5x + 2?
  5. 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