what is a line of rulers that passes power from father to son

It could be a hereditary monarchy or a dynasty.

It can also be primogeniture if the power and lands pass to the oldest son.

Please not #2 below which is taken from an online dictioary.

Main Entry: pri·mo·gen·i·ture
Function: noun
Pronunciation: -"chur, -ch&r, -"tyur, -"tur
Etymology: Late Latin primogenitura, from Latin primus + genitura birth, from genitus, past participle of gignere
1 : the state of being the firstborn of the children of the same parents
2 : an exclusive right of inheritance belonging to the eldest son