Why are two lines with the same y intercept are perpendicular?

The y-intercept doesn't really play a role in defining what a parallel or perpendicular line is it's just the point @ which the line crosses the y-axis (or the starting point), but in due case It might mean that they have the opposite slope but same y-intercept which is possible (see 1st picture as an EX)

If you want to know why 2 lines are perpendicular or parallel you have to look @ the slope 

Perpendicular: The slope is the negative reciprocal of the slope of the original equation (other line slope) what this means it that you flip the numerator and denominator and make it negative (or positive, depending if it's already negative)

Parallel: The slope is the same (see 2nd  picture as an EX).