Question

Determine whether this pair of lines is parellel, perpendicular, or neither 6+2x=3y 3x+2y=9 Choose the correct answer below. A. These two lines are perpendicular. B. These two lines are parallel C. These two lines are neither parallel nor perpendicular

Answer 1

Option A. These two lines are perpendicular

Explanation:

we know that

If two lines are parallel, then their slopes are equal

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

step 1

Convert the given equation A in slope intercept form

`y=mx+b`

where

m is the slope

b is the y-intercept

we have

`6+2x=3y` ----> equation A

Solve for y

That means----> isolate the variable y

Divide by 3 both sides

`y=(2)/(3)x+2`

so

`m_A=(2)/(3)`

step 2

Convert the given equation B in slope intercept form

`y=mx+b`

where

m is the slope

b is the y-intercept

we have

`3x+2y=9` ----> equation B

Solve for y

That means----> isolate the variable y

subtract 3x both sides

`2y=-3x+9`

Divide by 2 both sides

`y=-(3)/(2)x+4.6`

so

`m_B=-(3)/(2)`

step 3

Compare the slopes

`m_A=(2)/(3)`

`m_B=-(3)/(2)`

The slopes are opposite reciprocal (the product is equal to -1)

therefore

These two lines are perpendicular