What is the slope of a line that is perpendicular to a line whose equation is 3y=−4x+2 ?

The product of perpendicular line's slope (P) and the original line (I'm going to call it M) will always equal to minus one 

=> -1= M(P)

With the equation 
3y=-4x+2 
->The slope is -4/3
M= -4/3

-1=M(P)
P= -1/M
  = 
  = 4/3

The perpendicular slope is 3/4

For future reference (maybe?)
 ----> the perpendicular slope is the negative reciprocal of the original line's slope