How do you determine whether lines are parallel from their equations when given slope y intercept form?
and
how do you determine whether lines are perpendicular from their equations when given slope y intercept form?

Y= 1/3x+2
Y= 1/3x-9

These lines are parallel because the slopes are the same that's the number with the X . They never touch

Y= -1/2x+8
Y= 2x+ 8

If the X has opposite signs and they are reciprocal of each other like -1/2 and 2/1 they are perpendicular. They cross (intersect) each other and make a 90 degree angle. Perfect L shape when they cross each other they are perpendicular