What is the slope of a line that is perpendicular to the line whose equation is 3x+2y=6 3 x + 2 y = 6?

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