how do you find the slope and the y-intercept of the line 9y+3x+6=16+3x

9y+3x+6=16+3x

The equation is not simplified.
So group like terms, solve for y:
9y+3x+6=16+3x
9y+3x-3x=16-6
9y = 10
y=10/9
Since the x-term is missing from the equation, the equation represents a horizontal line, therefore the slope is zero.

The y-intercept is equal to 10/9.