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The problem you're working on requires finding a linear equation for the value $ V(t) $ of a product over time, given certain conditions:

### Information from the image:
- **2015 Value**: \$255,000
- **Rate**: \$800 decrease per year
- **Let $ t = 15 $ represent the year 2015**

### Step-by-Step Solution:

1. **Identify the form of the linear equation:**
   The linear equation for the value $ V(t) $ will follow the form:
   \[
   V(t) = V_0 + r(t - t_0)
   \]
   Where:
   - $ V_0 $ is the initial value (in 2015),
   - $ r $ is the rate of change (rate of decrease in this case),
   - $ t $ is the time in years since 2015.

2. **Insert the known values:**
   - $ V_0 = 255,000 $ (initial value in 2015),
   - $ r = -800 $ (since it's a decrease),
   - $ t_0 = 15 $ (since $ t = 15 $ corresponds to 2015).

   So the equation becomes:
   \[
   V(t) = 255,000 - 800(t - 15)
   \]

3. **Simplify the equation:**
   \[
   V(t) = 255,000 - 800(t - 15)
   \]
   Distribute the -800:
   \[
   V(t) = 255,000 - 800t + 12,000
   \]
   Combine like terms:
   \[
   V(t) = 267,000 - 800t
   \]

### Final Linear Equation:
\[
V(t) = 267,

You are given the dollar value of a product in 2015 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V(t) of the product in terms of the year t. (Let t = 15 represent 2015.)

This problem demonstrates how to write a linear equation to calculate the dollar value of a product over time, given a 2015 value of $255,000 and a yearly decrease of $800. Learn how to apply the formula V(t) = V_0 + r(t - t_0) for solving real-world scenarios. Suitable for students in Grades 9-12.

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