Question

The graph below illustrates the number of acres used for farming in Smalltown, New York, over several years.


Write a line of best fit equation. _______________

What does the slope mean in context?



What does the y-intercept mean in context?

Can you summarize you answer

Answer 1

To formulate a line of best fit equation, we would typically take the data points from the graph and use a method, such as linear regression, to determine the equation in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Since I cannot see the graph you mentioned, I will provide a general approach for each part of your question.

1. **Write a line of best fit equation**:
- You would need to determine the values for the slope (\( m \)) and the y-intercept (\( b \)) based on the graph. For example, if after analysis you found \( m = -10 \) and \( b = 200 \), the equation would be:
\[
y = -10x + 200
\]
- Note: Make sure to adjust the values according to your specific graph.

2. **Interpreting the slope**:
- The slope (\( m \)) represents the rate at which the number of acres used for farming changes over time. In the context of Smalltown, for example, if the slope is negative (like -10), it means that the number of acres used for farming decreases by 10 acres for each passing year.

3. **Interpreting the y-intercept**:
- The y-intercept (\( b \)) represents the estimated number of acres used for farming at the year when \( x = 0 \) (the starting point of your data). If the y-intercept is 200, this would indicate that in the initial year of measurement, there were approximately 200 acres operational for farming.

4. **Summary**:
- The line of best fit can be represented as \( y = mx + b \), where \( m \) indicates the change in the number of acres over time and \( b \) indicates the initial number of acres at the starting point of the analysis. For example, if slopes and intercepts were determined to be -10 and 200, it means that the number of acres used for farming is decreasing by 10 acres per year, starting from 200 acres.

This approach provides a basic understanding of how to interpret linear regression results in the context of agricultural land use. If you provide specific data points, I can help you create an exact equation and analyze it further!