The problem is to determine the most appropriate linear model for the data shown in the scatterplot. Let’s break it down:

Analysis:

1. Slope (m): The points in the scatterplot suggest a negative linear relationship because as $x$ increases, $y$ decreases.

2. Intercept (b): When $x = 0$, $y \approx 10$, which means the y-intercept is approximately 10.

3. Correct Equation Form: Given the slope is negative and the y-intercept is positive, the linear model must take the form $y = -1.9x + 10.1$.

Answer:

The correct choice is $\mathbf{B: y = -1.9x + 10.1}$.

Would you like a deeper explanation on how the slope and intercept are calculated?

Here are some questions to consider for further exploration:

1. How do you determine the slope of a line from two points?
2. What is the significance of a negative slope in a linear equation?
3. How do we identify the y-intercept in a graph?
4. Why is $y = -1.9x + 10.1$ the best fit for this scatterplot?
5. What methods exist to compute the equation of a line from a scatterplot in real-world data?

Tip: When analyzing scatterplots, always look for overall trends (positive, negative, or no correlation) to narrow down the appropriate model.