Explanation:
So to start
Perpendicular lines are lines that form 90 degree angles when they meet.
Parallel lines will never touch, no matter how far they go.
So
Top left
A vertical line and a horizontal line
This would be perpendicular
Lines that intersect to form right angles
As mentioned above this would be perpendicular
Two nonvertical lines that have a product of -1 for their slopes.
Parallel lines always have the same slope, so this goes for parallel.
Equations that can be written in slope intercept form
This would be both as all lines can be written in this form
Non vertical lines that have the same slope and different y-intercepts
As they have the same slope this would make it parallel
You can determine the relationship between two lines by comparing their slopes and y-intercepts.
This is both as this is a way to compare all lines
Lines in the same plane never intersect
This would be parallel
Slopes are opposite reciprocals
This is perpendicular as the slopes of perpendicular lines are reciprocals
Vertical lines that have different x-intercepts
This would be parallel
Sorry this is a lot
Hope this helped though :)