$(1)[10$ points$]$ Determine which of the following is an equation of the tangent line to the curve $y=\sqrt[\phantom{2}]{x}$ at the point $(9,3).$

$($A$)y=6x-51.$

$($B$)y=3x+24.$

$($C$)y=\frac{1}{6}x+\frac{3}{2}.$

$($D$)y=\frac{\sqrt[\phantom{2}]{x}}{2}-\frac{9}{2\sqrt[\phantom{2}]{x}}+3.$

Answer: