Explanation

(a) Since $\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \Rightarrow \frac{1}{v} = - \frac{1}{u} + \frac{1}{f}$
Putting the sign convention property
$\frac{1}{( - v)} = \frac{- 1}{( - u)} + \frac{1}{( - f)} \Rightarrow \frac{1}{v} = - \frac{1}{u} + \frac{1}{f}$
Comparing this equation with $y = mx + c$
Slope $= m = \tan\theta = - 1 \Rightarrow \theta = 135{^\circ}$ or $- 45{^\circ}$ and intercept $C = + \frac{1}{f}$