Which equation represents the depth of the lake, \( y \), based on the number of weeks passed, \( x \) ? \[ \begin{array}{l}\text { A. } y=-0.6 x+346 \\ \text { B. } y=-1.2 x+346 \\ \text { C. } y=-0.6 x \\ \text { D. } y=-1.2 x\end{array} \]

To determine which equation represents the depth of the lake \( y \) based on the number of weeks passed \( x \), let's analyze the given options: \[ \begin{array}{ll} \text{A. } y = -0.6x + 346 \\ \text{B. } y = -1.2x + 346 \\ \text{C. } y = -0.6x \\ \text{D. } y = -1.2x \\ \end{array} \] **Key Points to Consider:** 1. **Linear Relationship**: The equations are linear, implying a constant rate of change in the depth of the lake over time. 2. **Initial Depth**: Options A and B include a \( +346 \) term, suggesting an initial depth of 346 units (meters, feet, etc.), whereas C and D start at 0, implying no initial depth, which is unrealistic for a lake. 3. **Rate of Change**: - **Option A** has a slope of \(-0.6\), indicating the lake's depth decreases by 0.6 units per week. - **Option B** has a steeper slope of \(-1.2\), meaning the depth decreases by 1.2 units per week. - **Options C and D** also have negative slopes but lack the initial depth component. **Conclusion:** Without additional context or data specifying the rate at which the lake's depth changes, we typically assume that the more moderate rate is accurate unless there's evidence to suggest otherwise. Therefore, **Option A** is the most plausible choice as it accounts for both an initial depth and a reasonable rate of decrease. **Answer:** **A.** \( y = -0.6\,x + 346 \)