import numpy as np

def gradient_descent_vectorized(x, y, w, b, learning_rate, iterations):
    m = len(x)

    for _ in range(iterations):
        predictions = w * x + b
        errors = predictions - y

        slope_w = np.sum(errors * x) / m
        slope_b = np.sum(errors) / m

        w = w - learning_rate * slope_w
        b = b - learning_rate * slope_b

    return w, b


distances_np = np.array([1, 2, 3, 4, 5])
actual_times_np = np.array([12, 17, 22, 27, 32])

final_w, final_b = gradient_descent_vectorized(distances_np, actual_times_np, w=0, b=0, learning_rate=0.01, iterations=10000)

print("Final w:", final_w)
print("Final b:", final_b)

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