What is x=3y+6 converted into y intercept form

Okay so to convert x=3y+6 into y intercept form you need to first subtract x from both sides of the equation: 
x + 3y = 6 
(x + 3y) -x = 6 - x 

3y = -x + 6 <-- (Which is the same thing as 6-x, but with x in front) 

Now, to get rid of the 3 on the y side, divide by 3 on both sides of the equation (remember, what you do to one side you MUST do to the other side of the equation as well): 
(3y)/3 = (-x + 6)/3 

y = (-x/3) + 6/3 
or 
y = (-1/3)x + 2 (Same thing, don't forget the negative) 

y = mx + b 
So the slope is (-1/3) and the y-intercept, b, is 2. 

Hope you could understand that :3