(10,12) and is perpendicular to 5x+8y=1.

from 5x+8y = 1 

8y = -5x+1 

y = (-5/8)x+1/8 

slope is -5/8 

in perpendicular, new slope is 8/5 

then, point (10,12) 

y = mx+b,  

12 = (8/5)(10) + b  ==> b -4 

hence, y - (8/5)x-4 answer