Question

1. kylies math teacher finds that theres 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 $y = 58 + 7.8x$, where $y$ represents the expected quiz score and $x$ represents hours spent on homework that week. what is the meaning of the $x$-value when $y = 91$?

a. a students expected quiz score if they spent 91 hours on their homework.
b. the number of hours a student should spend on their homework to expect a score of 91 on the quiz.
c. a students expected quiz score if they spent no time on their homework.
d. the change in expected quiz score for every additional one hour students spend on their homework.

Explanation:

We know the equation \( y = 58 + 7.8x \), where \( y \) is the quiz score and \( x \) is hours spent on homework. When \( y = 91 \), we are finding the \( x \)-value. Let's analyze each option:

• Option A: If \( x = 91 \), we would be finding \( y \), but here \( y = 91 \), so this is incorrect.
• Option B: We substitute \( y = 91 \) into the equation to find \( x \), which represents the hours needed to get a score of 91. This matches the meaning of solving for \( x \) when \( y = 91 \).
• Option C: When \( x = 0 \), we find \( y \), which is the score with no homework, not related to \( y = 91 \).
• Option D: The coefficient of \( x \) (7.8) represents the change in score per hour, not what \( x \) means when \( y = 91 \).

Answer:

B. The number of hours a student should spend on their homework to expect a score of 91 on the quiz.