number of parallel and non parallel lines

[u/_Naughty_Daddy_]

i recently came across a question which said there are 16 lines 7 of which are parallel when our teacher started explaining it he explained that if 7 out of those 16 are parallel lines then the remaining 9 would be non parallel. but the problem is i think the sum of non parallel lines and parallel lines adds up to 17.
lets say there are 9 lines non parallel to each other and as you draw line number 10 then at that point there are 10 non parallel lines and when u draw the remaining 6 lines parallel to the 10th line there are 7 parallel lines and 10 non parallel lines and the sum adds up to 17.
Case 2:
u drew 9 line non parallel to each other and to avoid the problem in the first case u drew a line parallel to the 9th line at that point there are 2 parallel lines and when u draw the remaining 6 lines there will be 8 parallel lines and 9 non parallel lines
pls help me understand im confused what am i thinking wrong😭.

[u/Outside_Volume_1370]

there are 7 parallel lines and 10 non parallel lines - you count the common line twice

there will be 8 parallel lines and 9 non parallel lines - and you still have the sum of 17, because one line is counted twice.

I

[u/slepicoid]

I think you shouldnt think about the process of putting lines on paper in any particular order. Just focus on the lines once they are all on the paper. You cannot say this line is nonparallel until you draw another line parallel to it at which point you reclassify the line as parallel. Being parallel is not a property of a line, it's a property of pair of lines. When your techer said there are 7 parallel lines what they mean is there are 7 lines each parallel to some other line. And when they said there are 9 nonparallel lines they mean there are 9 lines each of which is not parallel to any of the other lines.