y=1/3x+1

The equation of a straight line can be written as y = m*x + c where m is the slope and c is the y-intercept.

A perpendicular to this will have slope -1/m.

I'm not sure if the following is what you are looking for:

Your equation is y = (1/3)x + 1

The perpendicular will be in the form y = -3x + c

If it goes through (4, 1) then

1 = -3*4 + c so that c = 13

The equation of the perpendicular line passing through (4, 1) is therefore  y = -3x + 13