To solve this problem, we need to:

1. Find the Equation of the Line of Best Fit:

   • The scatter plot shows a negative correlation between time spent texting ($x$) and time spent exercising ($y$). As $x$ increases, $y$ decreases.
   • To approximate the line of best fit, let's estimate the slope and intercept by picking two points that seem to represent the trend well.

   From visual inspection, we can choose:

   • Point A: (1, 9)
   • Point B: (9, 1)

   Calculate the slope ($m$): $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 9}{9 - 1} = \frac{-8}{8} = -1$

   Calculate the intercept ($b$) using the point-slope form $y = mx + b$: $9 = (-1)(1) + b \Rightarrow b = 10$

   Equation of the line: $y = -x + 10$

2. Predict the Time Spent Exercising for 4 Hours of Texting:

   • Substitute $x = 4$ into the equation $y = -x + 10$: $y = -(4) + 10 = 6$

   Therefore, a student who spends 4 hours texting is predicted to spend approximately 6 hours exercising.

Final Answers:

• (a) Equation of the line of best fit: $y = -x + 10$
• (b) Predicted time spent exercising for 4 hours texting: 6 hours

Would you like more details on this solution or have any questions?

Related Questions:

1. How can we determine the strength of the correlation from a scatter plot?
2. What are some methods to find the line of best fit for more precise data points?
3. How does the slope of the line of best fit affect the interpretation of data?
4. How would outliers affect the line of best fit in a scatter plot?
5. What are alternative ways to approximate the line of best fit without visually inspecting points?

Tip:

For a more precise line of best fit, use statistical software or methods like least squares regression, especially with a larger dataset.