Question

would points 3,4 and 7,7 be parallel to 0,0 and -6,8

Answer 1

one way to find out is to find the slopes of your points....parallel lines will have the same slope.

slope = (y2 - y1) / (x2 - x1)
(3,4)...x1 = 3 and y1 = 4
(7,7) ..x2 = 7 and y2 = 7
now we sub
slope = (7 - 4) / (7 - 3)
slope = 3/4

now do the same thing with the other 2 points...

slope = (y2 - y1) / (x2 - x1)
(0,0)...x1 = 0 and y1 = 0
(-6,8)..x2 = -6 and y2 = 8
now we sub
slope = (8 - 0) / (-6 - 0)
slope = 8/-6
slope = - 4/3

as you can see the slopes are not the same. Therefore, the lines are not parallel. In fact, they are negative reciprocals of each other making them perpendicular.