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No, for if they were to be the same think of it as a y-intercept being basic coordinates on a graph and unless there is another variable such as consisting of that of 3-dimensions (rather than just a x and y axis) they would be intersecting making them basically cross at that point as well as the rest of the coordinates due to the requirement of the same slope.

Example:

In simple y=mx+b form the b is the basic y-intercept, varied by the coordinates of where it intersects therefore....

y=2x+5 definitely holds the coordinates (0,5)

While y=2x+5 also holds the same coordinates assuredly intersecting at (0,5)

Though if the line were to be y=2x+2 it would not hold the coordinates (0,5) and would rather hold that as of (0,2) making it parallel

-What everything basically stands on is the variation of the y-intercept (Anything but the exact same in most cases) as well as the consistency of slope so that in simple form it would bear the same "steepness".

P.S.

Sorry if I repeated myself a lot but the simple answer is No

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Q: Can the Y-intercepts of two parallel lines be the same?
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