Question
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
Ask by Ellis Simmons. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The number **6.5** represents the increase in quiz score for each extra hour spent on homework each week.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
The number 6.5 in the equation represents the increase in the expected quiz score for each additional hour spent on homework. Essentially, for every hour a student dedicates to homework, their quiz performance is expected to improve by 6.5 points. It’s a fantastic incentive for students to hit the books! In educational practice, the linear relationship depicted in this equation reinforces the idea that consistent study habits can significantly impact academic success. Teachers and students alike can utilize this model to set realistic homework goals and monitor progress, promoting a more focused approach to learning and assessment!
