$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ is the formula which relates u \& v
$\frac{1}{u}=\frac{1}{f}-\frac{1}{v}$
Slope of the this curve can be found by differentiation $-\frac{1}{ u ^{2}} du =0+\frac{ dv }{ v ^{2}}$
$\Rightarrow \frac{ dv }{ du }=-\frac{ v ^{2}}{ u ^{2}}$
$\frac{ dv }{ du }$ is the slope which is negative so either curve (c) or curve (a) is right.
Now the slope depends upon the value of u & vi.e. it keeps changing at every point as per the equation above.