"Find an equation of the straight line that is tangent to the graph of f(x)=sqroot(x+1) and parallel to x-6y+4=0."

I've found so far that the slope of sqroot(x+1)=1/(sqroot(x+1) + sqroot(x+1))

as well as the equation of the parallel line to be y=x/6 + 2/3.

How do I solve for the other equation now?