https://file.aiquickdraw.com/mathbot/file/1730215978968d43jkbj4.jpg

To approach this problem, let’s go through the two parts step-by-step based on the scatter plot shown.

### (a) Writing the Equation of the Line of Best Fit
The line of best fit, or the trend line, represents the approximate relationship between \( x \) (time spent watching TV) and \( y \) (time spent doing homework). To determine the equation:

1. **Identify two points** on the line that best represents the trend of the data points.
   - From the scatter plot, let’s approximate two points. For instance, we could pick a point like \( (4, 28) \) and another around \( (28, 6) \).
   
2. **Calculate the Slope (m):**
   The slope formula is:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Using points \( (4, 28) \) and \( (28, 6) \):
   \[
   m = \frac{6 - 28}{28 - 4} = \frac{-22}{24} \approx -0.92
   \]

3. **Determine the Y-Intercept (b):**
   Use the slope-intercept form of the line, \( y = mx + b \). Substitute one of the points, say \( (4, 28) \), and the slope \( m = -0.92 \):
   \[
   28 = -0.92(4) + b
   \]
   Solving for \( b \):
   \[
   28 = -3.68 + b \Rightarrow b \approx 31.68
   \]

4. **Equation of the Line:**
   The approximate equation for the line of best fit is:
   \[
   y = -0.92x + 31.68
   \]

### (b) Predicting Homework Time for 12 Hours of TV
Using the equation from part (a), substitute \( x = 12 \) (time spent watching TV) to find \( y \) (time spent doing homework):

\[
y = -0.92(12) + 31.68
\]
\[
y = -11.04 + 31.68 = 20.64
\]

### Answers:
1. **Equation of the line of best fit:** \( y = -0.92x + 31.68 \)
2. **Predicted homework time for 12 hours of TV:** 20.64 hours

Would you like a detailed explanation of any specific step? 

---

### Related Questions:
1. How would the line of best fit change if more students spent more time on homework than on TV?
2. Can we determine the correlation coefficient from the scatter plot alone?
3. How would you interpret a positive slope in the context of this data?
4. What other statistical methods could verify the accuracy of the line of best fit?
5. How would outliers affect the equation of the line of best fit?

#### Tip:
When approximating the line of best fit on a scatter plot, choosing points that are spread out along the trend line can lead to a more accurate slope calculation.

The scatter plot shows the time spent watching TV, x, and the time spent doing homework, y, by each of 24 students last week. Use the scatter plot to answer the following:

(a) Write an approximate equation of the line of best fit. Round the coefficients to the nearest hundredth.

(b) Using your equation from part (a), predict the time spent doing homework for a student who spends 12 hours watching TV. Round your prediction to the nearest hundredth.

Learn how to determine the line of best fit from a scatter plot showing the relationship between TV watching time and homework time for students. Calculate the equation and predict homework time for specific TV hours.

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