What is the relationship between two lines whose slopes are negative 3 and 1/3?

Two lines could either be intersecting, perpendicular or parallel to each other. You can tell if which of those apply to two lines by looking at their slopes. If the slopes are equal, then those are parallel lines such that they never intersect. If the one slope is a negative reciprocal to each other, then those are perpendicular lines, such that the lines form a right angle. If neither, they are intersecting. From the description, we can say that the two lines are perpendicular lines.