A student investigates the kinetics of the reaction represented by the balanced equation below.

\[ 2\text{ NO}(g) + \text{Br}_2(g) \rightarrow 2\text{ NOBr}(g) \]

To determine the experimental rate law, the student measures the initial rate of formation of \(\text{NOBr}(g)\) across three trials at \(298\text{ K}\), collecting the data shown in the following table.

Trial	Initial \([\text{NO}]\) (\(\text{M}\))	Initial \([\text{Br}_2]\) (\(\text{M}\))	Initial Rate of Formation of \(\text{NOBr}\) (\(\text{M}\cdot\text{s}^{-1}\))
\(1\)	\(0.10\)	\(0.10\)	\(1.2 \times 10^{-3}\)
\(2\)	\(0.20\)	\(0.10\)	\(4.8 \times 10^{-3}\)
\(3\)	\(0.20\)	\(0.20\)	\(9.6 \times 10^{-3}\)

Three different reaction mechanisms are proposed:

Mechanism I
Step 1: \(\text{NO}(g) + \text{Br}_2(g) \rightarrow \text{NOBr}_2(g)\) (slow)
Step 2: \(\text{NOBr}_2(g) + \text{NO}(g) \rightarrow 2\text{ NOBr}(g)\) (fast)

Mechanism II
Step 1: \(\text{NO}(g) + \text{Br}_2(g) \rightleftharpoons \text{NOBr}_2(g)\) (fast equilibrium)
Step 2: \(\text{NOBr}_2(g) + \text{NO}(g) \rightarrow 2\text{ NOBr}(g)\) (slow)

Mechanism III
Step 1: \(\text{Br}_2(g) \rightleftharpoons 2\text{ Br}(g)\) (fast equilibrium)
Step 2: \(\text{NO}(g) + \text{Br}(g) \rightarrow \text{NOBr}(g)\) (slow)

Based on the experimental data, which mechanism is consistent with the observed rate law, and why?