The slope of the tangent line to $f(x)$ at $x=$a can be found by evaluating the limit $m_{tan}=\underset{h0}{lim}\frac{f(a+h)-f(a)}{h}$ provided the limit exists. If using decimal approximations, round all values to within six decimal places.

Given $f(x)=\sqrt[\phantom{2}]{x+8},$ find the slope of the tangent line to $f(x)$ at $x=-2$ using the above definition. Then find the equation of the tangent line to $f(x)$ at $x=-2.$

a$.m_{tan}=$

b$.$ The equation of the tangent line to $f(x)$ at $x=-2$ in slope intercept form is $y=$