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?
Choose 1 answer:
Choose 1 answer:
(Choice A)   Slope and \[x\]-intercept
A
Slope and \[x\]-intercept
(Choice B)   Slope and \[y\]-intercept
B
Slope and \[y\]-intercept
(Choice C)   Slope and a point that is not an intercept
C
Slope and a point that is not an intercept
(Choice D)   \[x\]-intercept and \[y\]-intercept
D
\[x\]-intercept and \[y\]-intercept
(Choice E)   \[y\]-intercept and a point that is not an intercept
E
\[y\]-intercept and a point that is not an intercept
(Choice F)   Two points that are not intercepts
F
Two points that are not intercepts

To determine the correct answer, we will analyze the problem step by step.

### Given:
1. The ice sheet starts with a thickness of **2 meters** at the beginning (week 0).
2. After **3 weeks**, the thickness is reduced to **1.25 meters**.
3. We are tasked with identifying what specific information about the graph of this relationship is provided.

---

### Step 1: Recognizing the linear relationship
The ice thickness decreases at a constant rate, which indicates that this is a **linear relationship**. In general, a linear relationship can be written in the form:

\[
y = mx + b
\]

- \( y \) represents the ice thickness (in meters).
- \( x \) represents the time in weeks.
- \( m \) is the slope of the line (rate of change of thickness).
- \( b \) is the \( y \)-intercept (initial thickness at \( x = 0 \)).

---

### Step 2: Interpreting the information provided
From the problem:
1. At \( x = 0 \), the ice thickness \( y = 2 \).  
   - This gives the **\( y \)-intercept** \( b = 2 \).

2. At \( x = 3 \), the ice thickness \( y = 1.25 \).  
   - This gives a point \((3, 1.25)\) on the graph that is **not** an intercept.

3. The slope \( m \) (rate of change) can be calculated as:

\[
m = \frac{\text{change in } y}{\text{change in } x} = \frac{1.25 - 2}{3 - 0} = \frac{-0.75}{3} = -0.25
\]

Thus, the slope of the line is \( -0.25 \).

---

### Step 3: Identifying the answer
From the above steps, we know:
- The **slope** \( m = -0.25 \) is provided.
- The **\( y \)-intercept** \( b = 2 \) is also provided.
- A point on the graph \((3, 1.25)\), which is not an intercept, is mentioned.

Since the \( y \)-intercept and a point (that is not an intercept) are part of the information provided, the correct answer is:

### **Choice E: \( y \)-intercept and a point that is not an intercept**

---

### Do you want me to clarify any part of this solution? Let me know!

---

### Related Questions:
1. How do you calculate the \( x \)-intercept of this graph?
2. What does the slope of \( -0.25 \) mean in the context of the problem?
3. How long will it take for the ice to completely melt (thickness = 0)?
4. Write the equation of the line that models the relationship between \( x \) and \( y \).
5. What would the graph of this relationship look like?

### Tip:
When analyzing linear relationships, always identify the slope and intercepts first, as they provide critical information about the graph's behavior.

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 graph the relationship between the thickness of an ice sheet and time, using a linear equation. This problem covers the concept of slope and intercepts, and how to interpret the given data points to identify key features of the graph. Suitable for students in Grades 7-9.

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