Determine if the line y+x-2 = 0 and the line 6y-3x +8 = 0 are parallel, perpendicular, or neither.

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.