Why moving m,b instead using mean and then finding y-intercept

Hi, i am on lecture ’ Optimization using Gradient Descent - Least squares with multiple observations’ in lesson 2 and my question is

why are we moving both slope and y-intercept instead if we calculate mean of x datapoint and y datapoint will get one coordinate of slope and then just need to find the y-intercept only to draw linear regression line ? why is both m ,b iteration ?

If the data set is very large, or if there are very many features (this can be a very big number), the gradient descent method is more computationally efficient.