How will the voltage $\left(V\right)$ between the two plates of a parallel plate capacitor depend on the distance $\left(d\right)$ between the plates, if the charge on the capacitor remains the same?

From $C=\frac{q}{V}$

We have, $V=\frac{q}{C}=\frac{qd}{{\epsilon }_{0}A}$ or $V\propto d$

Hence, graph is a straight line. 

When both plates are touched $\left(d=0\right)$, system still have some capacity$\left(C\ne 0\right)$.

So, from $C=\frac{q}{V}$ we can see that at very small seperations $V\ne \infty$ or graph does
not have any values for very small $d$.

$\therefore$ $V$ versus $d$ graph is as shown below :