Math Problem Statement

Graph the following features:

Y-intercept = minus, 3−3

Slope = minus, start fraction, 2, divided by, 5, end fraction−52​

Solution

Define the new slope and y-intercept slope_new = -2 / 5 y_intercept_new = -3

Calculate the corresponding y values using the new line equation

y_new = slope_new * x + y_intercept_new

Create the plot for the new line

plt.figure(figsize=(8, 6)) plt.plot(x, y_new, label=f"y = {slope_new}x + ({y_intercept_new})", color='blue') plt.axhline(0, color='black', linewidth=0.8, linestyle='--') plt.axvline(0, color='black', linewidth=0.8, linestyle='--') plt.scatter(0, y_intercept_new, color='red', label="Y-intercept (-3)") plt.title("Graph of the Line with Negative Slope") plt.xlabel("x") plt.ylabel("y") plt.grid(color='gray', linestyle='--', linewidth=0.5) plt.legend() plt.show()Here is the graph of the line with the specified features:

  • Y-intercept: -3 (indicated in red on the graph

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Slope-intercept form: y = mx + b

Theorems

Slope definition
Y-intercept property in linear equations

Suitable Grade Level

Grades 7-10