Question Claire's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation \( y=66+6.5 x \), where \( y \) represents the expected quiz score and \( x \) represents hours spent on homework that week. What could the number 6.5 represent in the equation? Answer Attempt 2 out of 2

In the linear equation \( y = 66 + 6.5x \): - **\( y \)** represents the expected quiz score. - **\( x \)** represents the hours spent on homework that week. - **66** is the **y-intercept**, indicating the expected quiz score when no time is spent on homework. - **6.5** is the **slope** of the line. **Interpretation of 6.5:** The number **6.5** represents the **rate of change** in the expected quiz score for each additional hour spent on homework. Specifically, for every extra hour a student spends on homework in a week, their expected quiz score increases by **6.5 points**. **Example:** - If a student spends **2 hours** on homework (\( x = 2 \)): \[ y = 66 + 6.5(2) = 66 + 13 = 79 \] The expected quiz score would be **79**. - If a student spends **5 hours** on homework (\( x = 5 \)): \[ y = 66 + 6.5(5) = 66 + 32.5 = 98.5 \] The expected quiz score would be **98.5**. **Conclusion:** The number **6.5** in the equation \( y = 66 + 6.5x \) signifies that **for each additional hour** a student spends on homework, their **expected quiz score increases by 6.5 points**. **Answer:** It is the number of quiz points a student is expected to gain for each additional hour spent on homework each week.