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