Find the equation of the straight line that is tangent to the graph of f(x)=(x+1)^0.5 and parallel to x-6y+4=0

my attempt:

y=x^0.5+1^0.5

y'=0.5x^-0.5

M_t=0.5/sqrt(x)

not sure if I am doing it right and where to head from here..

please state the steps needed to finish this question. Thank you