Answer
$y=-\frac{1}{2}x+\frac{\ln (2)+1}{2}$
Work Step by Step
The given line can be written in the slope-intercept form as: $$y=2x-8$$ where the slope is $2$. The slope of the tangent line is perpendicular to the given line so the product of their slopes is $-1$: $$m\cdot 2=-1 \to m=-\frac{1}{2}$$ so: $$m=f'(x)=-e^{-x}=-\frac{1}{2} \to e^{-x}=\frac{1}{2} \to x=\ln 2$$ so the tangent line touch the curve of $f$ at $(\ln 2,\frac{1}{2})$ so the equation of the tangent line is: $$y=\frac{1}{2}-\frac{1}{2}(x-\ln 2)$$ $$y=-\frac{1}{2}x+\frac{\ln (2)+1}{2}$$
