Question

benjamins 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 $y = 8x + 57$, 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 $y = 98$?
answer
the number of hours a student should spend on their homework to expect a score of 98 on the quiz.
a students expected quiz score if they spent 98 hours on their homework.
the change in expected quiz score for every additional one hour students spend on their homework.
a students expected quiz score if they spent 1 hour on their homework.

Explanation:

We are given the linear equation \( y = 8x + 57 \), where \( y \) is the expected quiz score and \( x \) is the hours spent on homework. We need to find the meaning of the \( x \)-value when \( y = 98 \).

Step 1: Understand the variables

In the equation, \( y \) represents the expected quiz score and \( x \) represents the hours spent on homework.

Step 2: Analyze the situation when \( y = 98 \)

We are substituting \( y = 98 \) into the equation to find the corresponding \( x \)-value. This \( x \)-value will represent the number of hours a student needs to spend on homework to have an expected quiz score of 98.

Let's analyze each option:

• Option 1: "The number of hours a student should spend on their homework to expect a score of 98 on the quiz." This matches our analysis because we are finding \( x \) (hours) when \( y \) (score) is 98.
• Option 2: "A student's expected quiz score if they spent 98 hours on their homework." This is incorrect because \( y = 98 \) is the score, not the hours.
• Option 3: "The change in expected quiz score for every additional one hour students spend on their homework." This describes the slope (8), not the \( x \)-value when \( y = 98 \).
• Option 4: "A student's expected quiz score if they spent 1 hour on their homework." This would be found by substituting \( x = 1 \), not \( y = 98 \).

Answer:

The number of hours a student should spend on their homework to expect a score of 98 on the quiz.