Answer
$\\y=\frac{1}{4}x+\frac{3}{4}$
Work Step by Step
$\\f(x)=\sqrt {x-1}$
$\\f(x)={(x-1)}^{1/2}$
$\\f’(x)=\frac{1}{2}(x-1)^{\frac{-1}{2}}$
$\\f’(x)=\frac{1}{2\sqrt {x-1}}$
$\\f’(5)=\frac{1}{2\sqrt {5-1}}$
$\\f’(5)=\frac{1}{4}$
Apply to straight line equation (y-y1)=m(x-x1)
$\\y-2=\frac{1}{4}(x-5)$
$\\y-2=\frac{1}{4}x-\frac{5}{4}$
$\\y=\frac{1}{4}x+\frac{3}{4}$
