Why Do Neural Networks Use y = w * x + b?

A neuron in a neural network uses this equation:

y = w * x + b

Because real life usually has a starting value, not zero.

Think of it as:

Output = (rate × amount) + base value

Simple Real-Life Examples

1. Taxi Fare 🚕

• $5 per km
• $20 base fare

fare = 5 * km + 20

Even at 0 km, you still pay $20 → that’s b.

1. Salary 💰

• $10 per hour
• $100 fixed pay

salary = 10 * hours + 100

Work 0 hours? You still earn $100.

What This Means in Deep Learning

x → input

w → importance (rate)

b → starting value

y → output

Without + b, the model is forced to start at zero, which doesn’t match real data.