Find the equation of the perpendicular line of 3y - 6x + 9 = 0 and passes through the origin.

Let the equation of the line be
:

y- y1 = m ( x-x1)  where ( x1, y1) any point passes through the
line and m is the slope.

Given that the line passes through the
origin point

Then the line passes through the point ( 0,
0)

Let us substitute:

==> y- 0 =
m (x- 0)

==> y= mx

Now we will
find the slope:

Given the perpendicular line
:

3y - 6x + 9 =0

We will write in slope
form:

==> 3y = 6x - 9

==>
y= 2x - 3

Then the slope = 2

Then the
perpendicular slope = -1/2

Then
:

 y= (-1/2) x