Light Yagami's relationship with Ryuk in the anime "Death Note" greatly influences his decisions. Ryuk, being a Shinigami (death god) who gives Light the Death Note, serves as both a mentor and a tempter to Light. Ryuk's presence pushes Light to use the Death Note to achieve his goals of creating a new world order, as Ryuk's fascination with Light's actions encourages him to continue using the Death Note. However, Ryuk also reminds Light of the consequences of his actions and the potential dangers of abusing the power of the Death Note, ultimately leading Light to make decisions that are both strategic and morally complex.