The sca... plot shows the time spent studying, x, and the quiz score, y, for each of 24 students. (a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit. (b) Using your equation from part (a), predict the quiz score for a student who spent 50 minutes studying. Note that you can use the graphing tools to help you approximate the line.

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### Scatter Plot Analysis and Line of Best Fit

The scatter plot below shows the time spent studying, \( x \), and the quiz score, \( y \), for each of 24 students.

#### Tasks:

**(a) Write an approximate equation of the line of best fit for the data.** 
- It doesn't have to be the exact line of best fit. 

**(b) Using your equation from part (a), predict the quiz score for a student who spent 50 minutes studying.**

Note that you can use the graphing tools to help you approximate the line.

#### Scatter Plot Description:

- **X-axis (horizontal):** Time spent studying (in minutes), ranging from 0 to 100 minutes.
- **Y-axis (vertical):** Quiz score, ranging from 0 to 100.
- **Data Points:** Each '×' represents an individual student’s data on quiz score versus time spent studying.

![Scatter Plot](link-to-image)


#### Step-by-Step Guide:

1. **Analyzing the Scatter Plot:**
   - Observe the distribution of data points to identify the trend.
   - The general trend shows an increase in quiz scores with an increase in study time.

2. **Approximate the Line of Best Fit:**
   - You can use the graphing tools to draw a line that best approximates the trend observed in the data points.

3. **Determine the Equation:**
   - The equation of the line is generally in the form \( y = mx + b \).
   - Use two points on the line to solve for the slope \( m \) and the y-intercept \( b \).

4. **Predict the Quiz Score:**
   - Using the equation derived, substitute \( x = 50 \) to predict the quiz score for a student studying for 50 minutes.

#### Example:

1. **Drawing a Line:**
   - Consider two points that the line passes through: (10, 30) and (80, 90).
   
2. **Calculate the Slope \( m \):**
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{90 - 30}{80 - 10} = \frac{60}{70} \approx 0.857
   \]

3. **Determine the Y-Intercept \( b \):**
   - Use one of the points
Transcribed Image Text:### Scatter Plot Analysis and Line of Best Fit The scatter plot below shows the time spent studying, \( x \), and the quiz score, \( y \), for each of 24 students. #### Tasks: **(a) Write an approximate equation of the line of best fit for the data.** - It doesn't have to be the exact line of best fit. **(b) Using your equation from part (a), predict the quiz score for a student who spent 50 minutes studying.** Note that you can use the graphing tools to help you approximate the line. #### Scatter Plot Description: - **X-axis (horizontal):** Time spent studying (in minutes), ranging from 0 to 100 minutes. - **Y-axis (vertical):** Quiz score, ranging from 0 to 100. - **Data Points:** Each '×' represents an individual student’s data on quiz score versus time spent studying. ![Scatter Plot](link-to-image) #### Step-by-Step Guide: 1. **Analyzing the Scatter Plot:** - Observe the distribution of data points to identify the trend. - The general trend shows an increase in quiz scores with an increase in study time. 2. **Approximate the Line of Best Fit:** - You can use the graphing tools to draw a line that best approximates the trend observed in the data points. 3. **Determine the Equation:** - The equation of the line is generally in the form \( y = mx + b \). - Use two points on the line to solve for the slope \( m \) and the y-intercept \( b \). 4. **Predict the Quiz Score:** - Using the equation derived, substitute \( x = 50 \) to predict the quiz score for a student studying for 50 minutes. #### Example: 1. **Drawing a Line:** - Consider two points that the line passes through: (10, 30) and (80, 90). 2. **Calculate the Slope \( m \):** \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{90 - 30}{80 - 10} = \frac{60}{70} \approx 0.857 \] 3. **Determine the Y-Intercept \( b \):** - Use one of the points
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