The Mathematical Relationship Between Linear Equations, Derivatives, and AI

Most people see y = mx + c as just a simple linear equation.

But inside machine learning and neural networks, this equation becomes the foundation of prediction, learning, and optimization.

In this article, I’ll explain how linear equations relate to derivatives, integration, and AI systems.
1) Linear Equation
y = mx + c

2) Derivative
dy/dx = m

3) Integration
∫ m dx = mx + c

4) Neural Network Neuron
z = wx + b

5) Weight Update
w = w - η(dL/dw)