we know that
if two lines are parallel
then
the slopes are the same
we have
15x - 16y = 1
solve for y
16y=15x-1
y=(15/16)x-(1/16)
m=15/16
case A)
16x - 15y = 1
15y=16x-1
y=(16/15)x-(1/15)
m=16/15------> is not equal to 15/16
case B)
15x + 16y = 1
16y=1-15x
y=(1/16)-(15/16)x
m=-15/16-------> is not equal to 15/16
case C)
y = (15/16) x - 7
m=15/16---------> is equal to 15/16
so
this equation is parallel to 15x - 16y = 1
case D)
y = (16/15) x - 7
m=16/15-------> is not equal to 15/16
therefore
the answer is the option
C y = (15/16) x - 7
