Is it possible for two graphs that are parallel to share the same y-intercept

No they cant not share the same y intercept.

No

lines that are paralell have the same slope

y=mx+b

m=slope

for them to be parlell, they cannot be the same line

that means that they have to have a different b

b is y intercpet, it tells how far up or down the line is

if they hit at the same value of y, then they would be the same line

no