The given line has slope [tex] m=-3 [/tex]. The slope of the line perpendicular to this line is [tex] -\frac{1}{m} =\frac{1}{3} [/tex].
Its equation is [tex] y=\frac{1}{3} x+c [/tex]. Since this line passes through, [tex] (3,4) [/tex],
[tex] 4=\frac{1}{3} (3)+c\\ c=3 [/tex]
Thus the equation of the line in slope intercept form is [tex] y=\frac{1}{3} x+3 [/tex]
