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.

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.**