Question 174231
Rewriting each of the given equation into the "point-slope" form of
y = mx + b
.
Line a: -2x+y=4
y = 2x+4 
.
Line b: 2x+5y=2 
5y = -2x+2
y = (-2/5)x + 2/5
.
Line c: x+2y=4 
2y = -x + 4
y = (-1/2)x + 2
.
Since NO two lines have the same slope -- no lines are parallel.
Now, if two lines are "negative reciprocals" then they are perpendicular.
Slope of line a: 2
Slope of line c: -1/2
They are "negative reciprocals" -- 
that is, if you multiply the two slopes you'll get -1
.
Answer would be -- d) Lines a and c are perpendicular.