Given that P sqrt(V) and Q sqrt(V), we can write these as:

Given that $P \propto \sqrt{V}$ and $Q \propto \sqrt{V}$, we can write these as:

where $k_1$ and $k_2$ are constants of proportionality.

The given equation is $P = aQ + b$.
Substitute the expressions for $P$ and $Q$:

For this equation to hold true for all values of $V$, the coefficients of $\sqrt{V}$ on both sides must be equal, and the constant terms must be equal.
Comparing the coefficients of $\sqrt{V}$:

Solving for $a$:

Comparing the constant terms:

Without specific numerical values for $P$, $Q$, or $V$ (or additional data points), the constants $k_1$ and $k_2$ cannot be determined numerically. Therefore,