For a reaction `X to Y`, the graph of the product concentration (x) versus time (t) came out to be a straight line passing through the
origin. Hence and time would be the graph of `(d[X])/(dt)` and the time
would be

Options

A. straight line with a negative slope and an intercept on y-axis
B. straight linc with a positive slope and an intercept on y-axis
C. a straight line parallel to x-axis
D. a hyperbola.

Explanation

To solve the problem, we need to analyze the information given about the reaction \( X \to Y \) and the corresponding graphs.

### Step-by-Step Solution:

1. **Understanding the Graph of Product Concentration vs. Time**:
- We are given that the graph of product concentration \( [X] \) versus time \( t \) is a straight line passing through the origin. This indicates a linear relationship between concentration and time.

2. **Identifying the Order of Reaction**:
- A straight line passing through the origin in the graph of concentration vs. time suggests that the reaction follows zero-order kinetics. In zero-order reactions, the concentration of the reactant decreases linearly with time.

3. **Rate of Reaction**:
- For a zero-order reaction, the rate of reaction \( r \) is constant and can be expressed as:
\[ r = -\frac{d[X]}{dt} = k \]
- Here, \( k \) is the rate constant.

4. **Graph of Rate of Reaction vs. Time**:
- Since the rate of reaction is constant for a zero-order reaction, the graph of \( \frac{d[X]}{dt} \) (which is the rate of change of concentration with respect to time) versus time \( t \) will be a horizontal line (straight line parallel to the x-axis).
- This means that the value of \( \frac{d[X]}{dt} \) remains constant over time.

5. **Conclusion**:
- Therefore, the graph of \( \frac{d[X]}{dt} \) versus time \( t \) for the given reaction will be a straight line parallel to the x-axis.

### Final Answer:
The graph of \( \frac{d[X]}{dt} \) versus time \( t \) will be a straight line parallel to the x-axis.

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