The rate-determining step is the slowest step in the mechanism. Here, Step 1 is the slow step:
\[ \text{CH}_4 \rightarrow \text{C} + 2 \text{H}_2 \]
Step 3: Analyze the rate law based on the rate-determining step
Since the rate-determining step involves \(\text{CH}_4\), the rate law will be dependent on the concentration of \(\text{CH}_4\):
\[ \text{Rate} = k[\text{CH}_4] \]
Final Answer
The correct graph representing how the reaction rate changes with the concentration of \([\text{CH}_4]\) is the one that shows a linear relationship, which is option (a).