Are those dots meant to indicate a repeating, periodic digit? Then the standard syntax is more complicated and uses FromDigits
:
RegionIntersection[
InfiniteLine[{{15, 158},
{FromDigits[{{73, 6, {7}}, 1}],
FromDigits[{{200, 6, {7}}, 1}]}}],
InfiniteLine[{{0, 193}, {300, 193}}]]
N[%, 5]