Y=1/6x+1
y=-6x+2
is this perpendicular or parallel lines

Perpendicular.
Parallel lines will have the same slope (1/6 and 1/6 or -6 and -6)
Perpendicular lines will have opposite reciprocal slopes. (1/6 and -6)

Y = 1/6x + 1
y = -6x + 2
1/6x + 1 = -6x + 2
 +6x          +6x      
6 1/6x + 1 = 2
             -1   -1
       6 1/6x = 1
6/37 × 37/6x = 1 × 6/37
                  x = 6/37
y = -6(6/37) + 2
y = -36/37 + 2
y = 1 1/37
(x, y) = (6/37, 1 1/37)