The slope of the line 4x + 5y =1 is m = -4/5. The slope of a line perpendicular to this line is the negative reciprocal of -4/5 . The negative reciprocal of -4/5 is 5/4
Thus a line perpendicular will have the equaiton
y = (5/4) x + b for any b.
Given one point on the line , b could be determined.