What is necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?

In order for a lines to be perpendicular to one another one of the lines must have the negative reciprocal slope from the other.

Explanation:

If the slopes of two lines are negative reciprocals of one another, then the two lines are perpendicular.

For example, if one line has a slope of 2, then its perpendicular line's slope is - 1/2.

If a a line's slope is 1/3, then its perpendicular line's slope is - 3/1