we have that
2y=-3x+6
isolate the variable y
Divide by 2 both sides
y=-(3/2)x+6/2
y=-1.5x+3
therefore
m=-1.5
b=3
For a parallel line, the slopes are equal ------> m=-1.5 or m=-3/2
For a perpendicular line, the slopes are negative reciprocal -----> m=2/3
equation of a parallel line could be y=-1.5x
equation of a perpendicular line could be y=(2/3)x
see the attached