https://file.aiquickdraw.com/mathbot/file/1729568661946kygeoln9.jpg

Let's break down the given problem.

### Key Information:
- Initially, the ice sheet is **2 meters thick**.
- After **3 weeks**, the ice sheet's thickness has decreased to **1.25 meters**.
- The thickness is decreasing **at a constant rate**, so we can model the relationship between thickness and time with a linear equation.

### Define Variables:
- Let \( y \) represent the thickness of the ice sheet (in meters).
- Let \( x \) represent the number of weeks that have passed.

### Steps to Approach:
1. **Find the slope (rate of change)**:  
   The thickness decreases from 2 meters to 1.25 meters in 3 weeks, so the slope \( m \) is calculated by the formula:
   \[
   m = \frac{\text{change in thickness}}{\text{change in time}} = \frac{1.25 - 2}{3 - 0} = \frac{-0.75}{3} = -0.25
   \]
   The slope \( m = -0.25 \), meaning the ice sheet's thickness decreases by 0.25 meters each week.

2. **y-intercept**:  
   The initial thickness is 2 meters when \( x = 0 \), so the y-intercept is 2.

### Graph Interpretation:
- **Slope**: The slope is known to be \( -0.25 \).
- **y-intercept**: The y-intercept is 2 because that is the starting thickness.

### Conclusion:
The graph of the relationship is a line with a slope of \( -0.25 \) and a y-intercept of 2. Therefore, the answer is **(B) Slope and y-intercept**.

Would you like more details or further clarification?

Here are five questions to deepen understanding:
1. How would the graph change if the ice melted faster?
2. What does the x-intercept of this graph represent physically?
3. How would you find the x-intercept from the equation?
4. Could this scenario ever have a positive slope?
5. How would the equation change if the rate of melting was not constant?

**Tip**: In linear models, the y-intercept often represents the starting value, and the slope shows how the dependent variable changes per unit of the independent variable.

A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 3 weeks, the sheet is only 1.25 meters thick. Let y represent the ice sheet's thickness (in meters) after x weeks. Which of the following information about the graph of the relationship is given?

Learn how to interpret the graph of a linear relationship where the thickness of an ice sheet decreases at a constant rate. The problem involves key mathematical concepts like slope and y-intercept, suitable for Grades 8-10 students.

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