https://file.aiquickdraw.com/mathbot/file/1727371025778uamp14nd.jpg

The scatterplot shows a clear downward trend, indicating a negative slope for the linear model. To find the most appropriate equation:

1. The slope \( m \) of the line appears to be negative since the \( y \)-values decrease as the \( x \)-values increase.
2. The data points suggest that the slope is around \(-1.9\), since for every unit increase in \( x \), \( y \) decreases by approximately 1.9 units.
3. The \( y \)-intercept (the value of \( y \) when \( x = 0 \)) is around 10, so the intercept is close to +10.

Given these observations, the most appropriate linear model would have a slope of \(-1.9\) and a \( y \)-intercept of 10, which corresponds to option **B: \( y = -1.9x + 10.1 \)**.

Would you like further details or have any questions about this?

Here are 5 related questions you can explore:
1. How can you determine the slope of a line from a scatterplot?
2. What is the significance of the \( y \)-intercept in linear models?
3. How do you differentiate between positive and negative slopes visually?
4. How can linear regression be used to find the exact line of best fit?
5. What role does the correlation coefficient play in determining linearity?

**Tip**: Always check if the data points suggest a linear trend before applying a linear model.

Which of the following equations is the most appropriate linear model for the data shown in the scatterplot?

Learn how to identify the best linear equation to model a scatterplot with a negative slope. This problem focuses on applying the slope-intercept form and analyzing data trends to find the most appropriate equation. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation