How is gradient descent and model optimization used in linear regression?

Focus on explaining the concept of gradient descent as an iterative optimization algorithm used to minimize the cost function in linear regression. Describe how it adjusts the model parameters (weights) to reduce the difference between predicted and actual values. Be prepared to detail the steps involved in gradient descent, including the calculation of the gradient and the learning rate's role. Additionally, discuss how this process leads to finding the optimal parameters that define the best-fitting line for the data. Use specific examples or mathematical expressions to illustrate your points clearly.