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The scatter plot shows the time spent watching TV, , and the time spent doing homework, y, by each of 24 students last week. (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 time spent doing homework for a student who spends 12 hours watching TV.
Note that you can use the graphing tools to help you approximate the line. (a) Write an approximate equation of the line of best fit. b) Using your equation from part (a), predict the time spent doing homework for a student who spends 12 hours watching TV.

To analyze the scatter plot and find the approximate equation of the line of best fit, we can follow these steps:

### (a) Approximate Equation of the Line of Best Fit
1. **Identify two points that lie close to the line of best fit.** From the scatter plot, it seems that the points \((0, 24)\) and \((32, 0)\) are good candidates.

2. **Calculate the slope \(m\)** using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Plugging in the values:
   \[
   m = \frac{0 - 24}{32 - 0} = \frac{-24}{32} = -\frac{3}{4} = -0.75
   \]

3. **Use the slope-point form of a line equation**, \(y - y_1 = m(x - x_1)\), to find the equation. Using the point \((0, 24)\), we get:
   \[
   y - 24 = -0.75(x - 0)
   \]
   Simplifying:
   \[
   y = -0.75x + 24
   \]

So, the approximate equation of the line of best fit is:
\[
y = -0.75x + 24
\]

### (b) Predict the Time Spent Doing Homework for 12 Hours of TV
Using the equation from part (a), we can predict the time spent doing homework when the time spent watching TV (\(x\)) is 12 hours:
\[
y = -0.75(12) + 24
\]
\[
y = -9 + 24 = 15
\]

**Prediction:** A student who spends 12 hours watching TV is predicted to spend approximately **15 hours** doing homework.

### Would you like more details or have any questions?

### Related Questions:
1. How does the slope of the line represent the relationship between TV watching and homework time?
2. What is the significance of the y-intercept in this context?
3. Can you explain how the line of best fit might change if more data points were added?
4. What does a negative slope indicate about the relationship between TV watching and homework time?
5. How accurate is a linear model for predicting the time spent on homework based on TV watching time?
6. What other types of relationships could exist between these two variables?
7. How would you calculate the exact line of best fit using statistical methods like least squares?
8. What are some factors that might cause deviations from this predicted relationship?

### Tip:
When approximating the line of best fit, it's helpful to choose points that are spaced apart and reflect the overall trend of the data.

Learn how to approximate the equation of the line of best fit from scatter plot data and predict homework time based on TV watching hours. This problem covers statistical concepts, including linear regression and the equation of a line. Suitable for Grades 9-12.

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