The problem involves modeling with linear functions, specifically looking at depreciation of an item over time. Let’s break it down based on the image.

Problem Setup:

• Scenario: A company purchases a machine for $87,500.
• Task: The depreciation data over several years is given in the table.

Table (Years $x$ vs Machine Value $y$):

• Year 0: $87,500
• Year 1: $75,625
• Year 2: $63,750
• Year 3: $51,875
• Year 4: $40,000
• Year 5: $28,125
• Year 6: $16,250
• Year 7: $4,375

Part A:

• Determine the type of function represented by the data: The data suggests a linear depreciation, as the machine's value decreases by a fixed amount each year. We can confirm this by calculating the depreciation per year and verifying that it's consistent.

Let me calculate the depreciation per year to check the linearity of the model.The depreciation per year is a consistent decrease of $11,875, confirming that the function represented by the data is linear.

Part A Answer:

The machine's value depreciates linearly, as shown by the consistent reduction of $11,875 per year.

Would you like to proceed with the next parts of the problem, or would you like additional details or clarification on this part?

Follow-up Questions:

1. How would you write the linear equation representing this depreciation?
2. What is the slope of the line representing this depreciation?
3. How would you graph this linear function using the data points?
4. How can you predict the machine's value after 10 years using the linear equation?
5. What is the significance of the y-intercept in this context?

Tip: When working with linear models, always check the consistency of the change (rate of change) to ensure the relationship is linear.