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From the scatter plot, you are asked to:

1. **Write an approximate equation of the line of best fit**. This equation typically follows the form \( \hat{y} = mx + b \), where \(m\) is the slope and \(b\) is the y-intercept.
   
   Looking at the plot:
   - The general trend is downward, meaning the slope \(m\) will be negative.
   - For instance, when \( x = 0 \), \( y \) seems to be around 9, suggesting the y-intercept \(b \approx 9\).
   - From point estimates, a rough slope can be found by picking two points, such as \((2, 7)\) and \((8, 3)\), and calculating:
     \[
     m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 7}{8 - 2} = \frac{-4}{6} = -\frac{2}{3}
     \]
     So, the slope \(m\) is approximately \(-\frac{2}{3}\).

   Therefore, the approximate equation of the line of best fit is:
   \[
   \hat{y} = -\frac{2}{3}x + 9
   \]
   Rounded to the nearest hundredth:
   \[
   \hat{y} = -0.67x + 9
   \]

2. **Predict the time spent exercising when a student spends 6 hours texting** by substituting \( x = 6 \) into the equation:
   \[
   \hat{y} = -0.67(6) + 9 = -4.02 + 9 = 4.98
   \]
   So, the predicted time spent exercising is approximately **4.98 hours**.

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Would you like more details on how to calculate the slope or y-intercept?

Here are 5 related questions to further explore this:

1. How do you calculate the slope from any two points on a scatter plot?
2. What is the importance of the y-intercept in the equation of a line?
3. Can the line of best fit ever have a positive slope if the data suggests a negative correlation?
4. What would happen to predictions if the texting time were much higher, say 12 hours?
5. How can the accuracy of this line of best fit be checked?

**Tip:** When approximating a line of best fit, always pick points that are widely spread to reduce error in calculating the slope!

The scatter plot shows the time spent texting, x, and the time spent exercising, y, by each of 23 students last week. Write an approximate equation of the line of best fit and use it to predict the time spent exercising when a student spends 6 hours texting.

This problem involves analyzing a scatter plot of 23 students, comparing time spent texting and exercising. Learn how to write the equation of the line of best fit and predict exercising time for 6 hours of texting. Key concepts include algebra, linear regression, and the slope formula.

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