I suppose you mean 3x + 5y = 1
Rearranging, we have:
5y = -3x + 1
y = (-3/5)x + (1/5)
The slope of this line is thus -3/5.
The slope of a line perpendicular to this line will be -1 / (-3/5) = 5 / 3
Using the slope formula, the line which we need will be:
(y - 6) / (x - 1) = 5 / 3
y - 6 = (5/3)(x - 1)
y - 6 = (5/3)x - (5/3)
y = (5/3)x + 6 - (5/3)
y = (5/3)x + (13/3)