Answer
$y$ = $\frac{1}{2}x+2$
Work Step by Step
$y$ = $\sqrt {x^{2}-x+7}$
$y(2)$ = $\sqrt {(2)^{2}-2+7}$ = $3$
$y'$ = $\frac{2x-1}{2\sqrt {x^{2}-x+7}}$
$y'(2)$ = $\frac{2(2)-1}{2\sqrt {(2)^{2}-2+7}}$ = $\frac{1}{2}$
$y'$ = slope = m
$y-y_{1}$ = $m(x-x_{1})$
$y-3$ = $\frac{1}{2}(x-2)$
$y$ = $\frac{1}{2}x+2$
