You have 3 attempts on this assignment. We can go over any questions that you have in group session. Soclologists surveyed randomly selected students who took a college entrance exam about the number of hours of television they watch dally and their score on the exam. With their finding, the sociologists made a scatter plot and found that a line with the equation $$ y=-0.75 x+36 $$ best models the data, where $$ x $$ is the number of hours of television watched, and y is the exam score. Which statement is definitely true base on the equation? No student's exam score was 36 . One student's exam score was 36 For every 3 hours of television watched, a student's exam score decreased by 4 points. For every 4 hours of television watched, a student's exam score decreased by 3 points.

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Based on the equation $$ y = -0.75x + 36 $$:

- **Slope Interpretation**: The slope $$-0.75$$ indicates that for each additional hour of television watched ($$ x $$), the exam score ($$ y $$) decreases by 0.75 points.

Let's evaluate each statement:

1. **No student's exam score was 36.**
   - *Incorrect.* The equation suggests that if a student watched 0 hours of television, their predicted exam score would be 36. However, this doesn’t guarantee that no student actually scored 36.

2. **One student's exam score was 36.**
   - *Incorrect.* While the model predicts a score of 36 when $$ x = 0 $$, it doesn't confirm that an actual student had this exact score.

3. **For every 3 hours of television watched, a student's exam score decreased by 4 points.**
   - *Incorrect.* Using the slope:
     $$
     3 \text{ hours} \times -0.75 \text{ points/hour} = -2.25 \text{ points}
     $$
     This does not equal a 4-point decrease.

4. **For every 4 hours of television watched, a student's exam score decreased by 3 points.**
   - *Correct.* Using the slope:
     $$
     4 \text{ hours} \times -0.75 \text{ points/hour} = -3 \text{ points}
     $$
     This matches the statement exactly.

**Therefore, the statement that is definitely true based on the equation is:**

**For every 4 hours of television watched, a student's exam score decreased by 3 points.**
For every 4 hours of television watched, a student's exam score decreased by 3 points.

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