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
