A question about linear transformations mapping straight lines to straight lines Obviously, a linear transformation over a space maps all straight lines to other straight lines.

My question is: is the converse true? That is, if we're looking at a space after some transformation and we're observing that all straight lines were mapped to straight lines, does that imply a linear transformation? (Lines are understood as finite and infinite collections of points that are aligned, well, in a line)

EDIT: The comments mention affine transformations which fullfil the above condition but are not linear since they also involve translation. I think I'll reask then: Is every transformation that maps ALL lines to lines necessarily affine?
not always but converse will  be true iff T(x) that is a function of x .You can suppose y=T(x) represents the line that Passes through origin
not always but converse will  be true iff T(x) that is a function of x .You can suppose y=T(x) represents the line that Passes through origin