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