(1) The line y = mx – c passes through the point (p, q).
Line y=mx-c is parallel to y=mx+c but they are same when c=0 which is not the case.
so no intersection point exists.
If (p,q) lie on line y=mx+c => (p,q) does not lie on y=mx-c
SUFFICIENT

(2) The line y = –mx + c passes through the point (p, q).
Intersection point of y=mx+c and y=-mx+c is (0,c)
Since p<>0 indicates that (p,q) is not the intersection point of lines y=mx+c and y=-mx+c.
If (p,q) lie on line y=mx+c => (p,q) does not lie on y=-mx+c
SUFFICIENT

D