https://file.aiquickdraw.com/mathbot/file/1726454151072yj4wb5zc.jpg

The problem in the image involves writing a linear equation that represents the dollar value of a product over time. Here's the breakdown:

### Given Information:
- **Initial value in 2015 (when $ t = 0 $):** $ \$255,000 $
- **Rate of decrease per year:** $ \$5,600 $ per year
- The equation for the value $ V(t) $ of the product after $ t $ years is linear and in the form:
  \[
  V(t) = -5600t + 344000
  \]

The image explains that $ t $ is the number of years after 2015. So, the equation models the decreasing value of the product over time, starting at $ \$344,000 $ in 2015 and decreasing by $ 5600 $ each year.

### Explanation:
- **Slope (-5600):** This represents the annual decrease in the product's value.
- **Intercept (344,000):** This is the initial value of the product in 2015 before the yearly decreases start.

Would you like me to go further into solving a related question or explain more about how to interpret the equation?

### 5 Related Questions:
1. What will the value of the product be in 2020 (5 years after 2015)?
2. In how many years will the value of the product reach $ \$0 $?
3. How does the slope of this equation relate to the rate of decrease?
4. How can we graph this equation to visualize the decrease in value over time?
5. What would happen if the rate of decrease changed to $ \$10,000 $ per year instead?

### Tip:
Always check the units and ensure you're interpreting the year $ t $ correctly when dealing with real-world problems like this one.

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 of the product in terms of the year t.

Learn how to write a linear equation representing the value of a product decreasing by $5600 per year, starting from $344,000 in 2015. The problem covers algebraic concepts, focusing on creating and interpreting linear equations.

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