Question

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

Answer 1

The slope of the line perpendicular to the given line is 2/3

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