The scatterplot shows a positive linear relationship between the number of hours studied (x-axis) and test scores (y-axis). To determine the most appropriate equation for the line of best fit, consider the slope (rate of change) and the y-intercept.

Key Observations:

1. Positive slope: The data shows that as the number of hours studied increases, the test scores increase. This indicates a positive slope.
2. Intercept: At approximately $x = 0$, $y$ seems to be around 60, suggesting the y-intercept is close to 60.

Equation Analysis:

1. $y = -10x + 30$: Incorrect, as it has a negative slope and doesn't fit the upward trend.
2. $y = 10x + 60$: Likely correct, as it has a positive slope of 10 and a y-intercept of 60.
3. $y = 10x + 30$: Incorrect, as the y-intercept (30) is too low compared to the scatterplot.
4. $y = -10x + 60$: Incorrect, as it has a negative slope.

Answer:

The most appropriate linear model is: $\boxed{y = 10x + 60}$

Would you like a detailed explanation of how to compute the slope and intercept from data points?

5 Related Questions:

1. How do you calculate the slope of a line from data points?
2. What is the significance of the y-intercept in a linear equation?
3. How can you verify if a line fits a scatterplot using residuals?
4. What are alternative methods to determine the best-fit line, like least squares regression?
5. How does the slope influence predictions in a linear model?

Tip: The y-intercept represents the predicted outcome when the independent variable is zero. Always check this against the graph!