Given the lines:
y + x -2 = 0
6y-3x + 8 =0
We need to determine the relation between the lines ( parallel, perpendicular, or neither)
First we will use the slope to find the relation.
If the slopes are equal, then the lines are parallel.
if the product of the slopes is -1, then the slope are perpendicular.
Let us rewrite the equations of the lines into the slope form.
==> y = -x + 2 ............(1)
==> y = (3/6)x - 8/6
==> y= (1/2)x - 4/3........(2)
We notice that the slopes are not equal. then the lines are not parallel.
Also, the product of the slopes is -1*1/2 = -1/2 , then the lines are not perpendicular.
Then the slopes are not parallel nor perpendicular.