Answer:
Option A. These two lines are perpendicular
Step-by-step 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
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]6+2x=3y[/tex] ----> equation A
Solve for y
That means----> isolate the variable y
Divide by 3 both sides
[tex]y=\frac{2}{3}x+2[/tex]
so
[tex]m_A=\frac{2}{3}[/tex]
step 2
Convert the given equation B in slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]3x+2y=9[/tex] ----> equation B
Solve for y
That means----> isolate the variable y
subtract 3x both sides
[tex]2y=-3x+9[/tex]
Divide by 2 both sides
[tex]y=-\frac{3}{2}x+4.6[/tex]
so
[tex]m_B=-\frac{3}{2}[/tex]
step 3
Compare the slopes
[tex]m_A=\frac{2}{3}[/tex]
[tex]m_B=-\frac{3}{2}[/tex]
The slopes are opposite reciprocal (the product is equal to -1)
therefore
These two lines are perpendicular
