# Lines covering all lattice points

$$S$$ is a set of lines in $$\mathbf{R}^2$$, each of which passes through the origin. Every lattice point $$(x,y)$$ such that $$0 \leq x,y \leq 5$$ is on at least one line in $$S$$. What is the minimum size of $$S$$?

Details and assumptions

A lattice point $$(x,y)$$ satisfies the condition that $$x$$ and $$y$$ are integers.

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