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We are given the equation of the line of best fit, which is \( y = -0.75x + 8.65 \), where:
- \( x \) represents the time spent texting (in hours),
- \( y \) represents the time spent exercising (in hours).

Let's solve each question based on this equation.

### (a) What is the predicted time spent exercising for a student who spends 4 hours texting?

Substitute \( x = 4 \) into the equation:

\[
y = -0.75(4) + 8.65 = -3 + 8.65 = 5.65 \text{ hours}
\]

Thus, the predicted time spent exercising is **5.65 hours**.

---

### (b) What is the predicted time spent exercising for a student who doesn't spend any time texting?

Substitute \( x = 0 \) into the equation:

\[
y = -0.75(0) + 8.65 = 8.65 \text{ hours}
\]

Thus, the predicted time spent exercising is **8.65 hours**.

---

### (c) For an increase of one hour in the time spent texting, what is the predicted decrease in the time spent exercising?

The slope of the line \( -0.75 \) represents the rate of change. For each 1-hour increase in texting, the predicted time spent exercising decreases by **0.75 hours**.

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Let me know if you would like more details, or if you have any questions!

Here are 5 related questions to deepen understanding:

1. How would the time spent exercising change for a student who spends 7 hours texting?
2. If the slope of the line were steeper (e.g., \( -1 \)), how would this impact the relationship between texting and exercising?
3. What is the meaning of the y-intercept in this context (i.e., \( 8.65 \))?
4. Could the trend line be used to predict time spent exercising for a student who texts for 12 hours? Why or why not?
5. How would the graph look if there was no correlation between texting and exercising?

**Tip:** The slope of a line represents the rate of change, which is key in interpreting relationships between two variables.

The scatter plot shows the time spent texting (x) and the time spent exercising (y) by each of 24 students last week. The equation of the line of best fit is y = -0.75x + 8.65. Using this equation, answer the following questions:
(a) What is the predicted time spent exercising for a student who spends 4 hours texting?
(b) What is the predicted time spent exercising for a student who doesn't spend any time texting?
(c) For an increase of one hour in the time spent texting, what is the predicted decrease in the time spent exercising?

This problem uses the equation of a line of best fit, y = -0.75x + 8.65, to predict the time spent exercising based on the time spent texting. Students solve for exact values and understand the relationship between variables through the slope of the line. Suitable for Grades 7-10.

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