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To calculate the residual for the data point at \( (1.5, 61) \):

1. **Identify the point and the line of best fit:** 
   - We have a data point where \( x = 1.5 \) hours and the observed \( y \)-value (score) is 61.

2. **Determine the expected \( y \)-value on the line of best fit at \( x = 1.5 \):**
   - The line of best fit appears to pass through two known points: \( (0, 55) \) and \( (4.5, 85) \).

3. **Calculate the slope of the line of best fit:**  
   \[
   \text{slope} = \frac{85 - 55}{4.5 - 0} = \frac{30}{4.5} \approx 6.67
   \]

4. **Write the equation of the line of best fit:**  
   Using the point-slope form \( y = mx + b \), with \( m = 6.67 \) and passing through \( (0, 55) \), we find:
   \[
   y = 6.67x + 55
   \]

5. **Calculate the predicted \( y \)-value at \( x = 1.5 \):**  
   \[
   y = 6.67(1.5) + 55 = 10.005 + 55 = 65.005
   \]

6. **Calculate the residual:**  
   Residual = Observed \( y \)-value - Predicted \( y \)-value  
   \[
   \text{Residual} = 61 - 65.005 = -4.005
   \]

### Answer:
The residual for the data point at \( (1.5, 61) \) is approximately \( -4.005 \).

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Would you like more details on any of the steps? Here are related questions to deepen your understanding:

1. What does a negative residual indicate in the context of this problem?
2. How would the residual change if the observed score was higher than the predicted score?
3. How is the line of best fit determined in a scatter plot?
4. What is the significance of residuals in analyzing data fit?
5. How can residuals help us identify outliers in data?

**Tip:** A residual close to zero means the point is well-fitted to the line, while a large residual indicates a possible outlier.

Mamadou's math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. Calculate the residual for the data point that corresponds to 1.5 hours of study and a score of 61 points.

Learn how to calculate the residual for a data point in a scatter plot with the line of best fit. This example covers finding the residual for 1.5 hours of study with a score of 61, using the equation of the line derived from two points. Suitable for students in Grades 9-10.

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