Is there a difference in dilating lines when dilating polygon line equations versus dilating tangent lines to y=f(x) functions?

Question

Is there a difference in dilating lines when dilating polygon line equations versus dilating tangent line equations to y=f(x) functions?

If so then the dilation type for line y=mx+b needs to be specified.

Proposed answer, for polygon dilation of y=mx+b side,,,from any center,,,, line dilation must have same slope to preserve geometry similarity.

But for function (y-y₁)= f(x-x₁) , and dilation of y-y₁ variable, the corresponding

tangent line dilation from (x₁,y₁) center dilated in y-y₁ is a function dilation. And the

latter tangent line does not have same slope as original tangent line.

Agree or Disagree is the question?

Answer 1

agree with my own conclusion