Consider the function and the value $ofa.$

$f(x)=\frac{x}{2}+3,a=-1$

$(a)$ Use $m_{tan}=\underset{h0}{lim}\frac{f(a+h)-f(a)}{h}to$ find the slope $of$ the tangent line $m_{tan}=f^{\text{'}}(a).$

$m_{tan}=$

$(b)$ Find the equation $of$ the tangent line $tofatx=axbe$ the independent variable and $ybe$ the dependent variable.