Answer
$f(x)= 1/3*x+20/3$
Work Step by Step
Through the point $(-2,6)$ and perpendicular to $f(x)=-3x+4$
Perpendicular lines have slopes whose product is -1
$-3*x=-1$
$-3*x/-3=-1/-3$
$x=1/3$
$y=mx+b$
$6=1/3*-2+b$
$6=-2/3+b$
$6+2/3=-2/3+b+2/3$
$20/3=b$
$y=1/3*x+20/3$
$f(x)= 1/3*x+20/3$
