\(S\) 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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