There are just two parameters that determine a line completely: either two points that the line goes through, or a point and the slope of the line.
Then, if two lines both pass through the same point and have the same slope, then they are the same line (they intersect at infinitely many points).
Therefore, the statement "two lines that have the same y-intercept and the same slope, intersect at exactly one point" is not true for any cases.
