Consider the slope of each line, for a parallel line they will have the same slope. Parallel line have the same slope because they have to change at the same rate or else they would cross each other eventually right?

Perpendicular lines have slopes that are negative reciprocals of eachother i.e.

the negative reciprocal of If we multiplied these together we would get -1 that would be the case with all perpendicular lines, if you multiply the slopes together you should get -1