Month The equation for the line of best fit is $$ y=-\frac{1}{2} x+25 $$. According to the equation, which of these statements is true? The depth of the lake is expected to decrease about 1 foot every 2 months during the drought. The depth of the lake is expected to decrease about 2 feet every 1 month during the drought.

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UpStudy AI · Accepted Answer

The given equation for the line of best fit is:

$$ y = -\frac{1}{2}x + 25 $$

Here:
- $$ y $$ represents the depth of the lake.
- $$ x $$ represents the number of months.
- The slope of the line is $$-\frac{1}{2}$$, which indicates the rate at which the lake's depth is changing over time.

**Interpreting the Slope:**

- **Slope ($$ m $$) = $$-\frac{1}{2}$$**
  
  This means that for each additional month ($$ x $$), the depth ($$ y $$) decreases by $$\frac{1}{2}$$ foot.

**Evaluating the Statements:**

1. **"The depth of the lake is expected to decrease about 1 foot every 2 months during the drought."**
   
   - **Calculation:** 
     - In 2 months, the total decrease would be:
       $$
       \text{Decrease} = 2 \times \left(-\frac{1}{2}\right) = -1 \text{ foot}
       $$
   
   - **Conclusion:** This statement accurately reflects the rate of decrease as indicated by the slope.

2. **"The depth of the lake is expected to decrease about 2 feet every 1 month during the drought."**
   
   - **Calculation:**
     - In 1 month, the decrease would be:
       $$
       \text{Decrease} = 1 \times \left(-\frac{1}{2}\right) = -\frac{1}{2} \text{ foot}
       $$
   
   - **Conclusion:** This statement overstates the rate of decrease. The lake's depth decreases by $$\frac{1}{2}$$ foot each month, not 2 feet.

**Final Answer:**

**"The depth of the lake is expected to decrease about 1 foot every 2 months during the drought."** is the true statement according to the equation.
The depth of the lake is expected to decrease about 1 foot every 2 months during the drought.

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