  We prove a nontrivial energy bound for a finite set of affine transformations
over a general field and discuss a number of implications. These include new
bounds on growth in the affine group, a quantitative version of a theorem by
Elekes about rich lines in grids. We also give a positive answer to a question
of Yufei Zhao that for a plane point set P for which no line contains a
positive proportion of points from P, there may be at most one line, meeting
the set of lines defined by P in at most a constant multiple of |P| points.
