Find equation of line tangent to the hyperbola $\displaystyle \frac{2}{x}$ at the point $\displaystyle (4,1/2)$

I can't see where the y-intercept comes from...$\displaystyle f' = -2x^{-2} \Rightarrow f'(4) = -\frac{1}{8}$ so the equation is $\displaystyle y = -\frac{1}{8}x + ?$

I don't where to go from finding the slope, do I just keep plugging in points for $\displaystyle f'(x)$?????