Question

How can you determine if two lines are parallel, perpendicular, or neither ?

Answer 1

Two lines in a 2D space can be i) parallel ; ii) perpendicular or iii) neither parallel nor perpendicular

i) test to check if lines are parallel:
Extend the two lines on both its ends to see if they meet, if these two lines do not meet no matter how much you extend them then it can be said that these two lines are parallel
(or) compare the slopes of both lines, two parallel lines will have the same slope;  

ii) test to check if two lines are perpendicular:
draw a perpendicular to the first line and check if this perpendicular to the first line is parallel to the second line;
if two lines are perpendicular, then the perpendicular to one of the lines will be parallel to the other line;
(or) multiply the slopes of two lines to see if it comes out to be= -1;
product of the slopes of two perpendicular lines =-1

iii) if a pair of lines fail the parallel and perpendicular test then it can be said that they are neither parallel nor perpendicular;
(or) if the slopes of two lines are unequal and the product of their slopes is not equal to -1 then the lines are neither parallel nor perpendicular;