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]