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.

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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 $x = 0$).

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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 $-0.25$.

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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

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

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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.