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A straight line $L$ at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular from the origin to this line makes an angle of $60°$ with the line $x + y = 0$. Then an equation of the line $L$ is:
(1) $x + \sqrt{3}y = 8$
(2) $(\sqrt{3} + 1)x + (\sqrt{3} - 1)y = 3\sqrt{2}$
(3) $\sqrt{3}x + y = 8$
(4) $(\sqrt{3} - 1)x + (\sqrt{3} + 1)y = 8\sqrt{2}$
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