Answer:
The slope of the line perpendicular to the given line is 2/3
Step-by-step explanation:
step 1
Find the slope of the given line
we have
3x+2y=6
isolate the variable y
2y=-3x+6
y=-(3/2)x+3
The slope of the given line is m=-(3/2)
step 2
Find the slope of the line perpendicular to the given line
Remember that
If two lines are perpendicular, their slopes are opposite reciprocal of each other ( the product of their slopes is equal to -1)
so
m1*m2=-1
we have
m1=-3/2
so
m2=2/3
therefore
The slope of the line perpendicular to the given line is 2/3
