Answer
$L(x)=x+1$ at $x=x_{0}=8$
Work Step by Step
$f(x)=x+1 $,
$L(x)=f(a)+f'(a)(x-a)$
$f'(x)=1$
at $x_{0}=8$ the function and its derivative is close to the value 8.1
so $x_{0}=8$
$f(8)=8+1=9$
$f'(8)=1=1$
then $L(x)=9+(x-8)=x+1$
$L(x)=x+1$ at $x=x_{0}$
Thus, the final answer is: $L(x)=x+1$ at $x=x_{0}$
