[math-fun] least-squares derivation ?

In common discussions of least squares, the parameters (m,b) are estimated for the equation y = m*x+b using as data various datapoints [x1,y1], [x2,y2], [x3,y3], etc. For example, in Wikipedia (where m=beta2 and b=beta1): https://en.wikipedia.org/wiki/Linear_least_squares#Example So far, so good. Now, if I merely exchange x and y, then my equation is x = m'*y+b', where should be m' = 1/m and b' = -b/m. (Let's ignore the case where the best m=0.) However, if I then estimate (m',b') using the same least squares method, I don't get (1/m,-b/m) ! So either I'm doing something wrong, or perhaps there is a more symmetric least squares method that treats x and y symmetrically ??