Unconditional Love: It could refer to a more spiritual or unconditional type of love, possibly in the context of familial bonds, self-love, or love for humanity. "That line" could be understood as a metaphor for a path or connection that ties people together through love.
A Line in Time: Another interpretation could be that the "line" represents a moment or a phase in time, where love is at its forefront—maybe a pivotal experience or decision.