Why it is not possible for two lines to be parallel and perpendicular?

Parallel lines have the same slope. for example, the two lines y = 6x + 3 and

y = 6x - 5 are parallel because they have the same slope, 6x.

the slopes of perpendicular lines are opposite reciprocals, which means that you would flip the numbers of the fraction and make it negative. for example, the opposite reciprocal of - 3x is 1/3x.

also, parallel lines never intersect, whereas perpendicular lines intersect at a 90 degree angle.

therefore, it isnt possible for two lines to be both parallel and perpendicular.