Find an Equation of the Tangent Line at the Indicated $$w = g ( z ) = 4 + \sqrt { 6 - z } , ( z , w ) = ( 5,5 )$$

Multiple Choice

Find an equation of the tangent line at the indicated point on the graph of the function.
- $$w = g ( z ) = 4 + \sqrt { 6 - z } , ( z , w ) = ( 5,5 )$$

A) $w = - \frac { 1 } { 2 } z - \frac { 15 } { 2 }$
B) $w = \frac { 1 } { 2 } z + \frac { 15 } { 2 }$
C) $w = - \frac { 1 } { 2 } z + \frac { 15 } { 2 }$
D) $w = \frac { 1 } { 2 } z - \frac { 15 } { 2 }$