Question

question
carloss 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 = 61 + 7.6x ), 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 = 92 )?
answer
the number of hours a student should spend on their homework to expect a score of 92 on the quiz.
the change in expected quiz score for every additional one hour students spend on their homework.
a students expected quiz score if they spent 92 hours on their homework.
a students expected quiz score if they spent no time on their homework.

Explanation:

Step1: Understand the equation

The given equation is \( y = 61 + 7.6x \), where \( y \) is the expected quiz score and \( x \) is the hours spent on homework. We need to find the meaning of \( x \) when \( y = 92 \).

Step2: Substitute \( y = 92 \) into the equation

Substitute \( y = 92 \) into \( y = 61 + 7.6x \), we get \( 92 = 61 + 7.6x \).

Step3: Solve for \( x \)

First, subtract 61 from both sides: \( 92 - 61 = 7.6x \), which simplifies to \( 31 = 7.6x \). Then, divide both sides by 7.6: \( x=\frac{31}{7.6}\approx 4.08 \)? Wait, no, wait. Wait, the question is about the meaning of \( x \) when \( y = 92 \), not the value. Wait, the options are about the meaning. Let's re - evaluate.

The equation is a linear model where \( y \) is the quiz score and \( x \) is the hours of homework. When we set \( y = 92 \), we are solving for \( x \), which represents the number of hours a student should spend on homework to have an expected quiz score of 92? Wait, no, let's look at the options.

Wait, the options:

1. The number of hours a student should spend on their homework to expect a score of 92 on the quiz.

1. The change in expected quiz score for every additional one hour students spend on their homework. (This is the slope, 7.6, so not related to \( x \) when \( y = 92 \))

1. A student’s expected quiz score if they spent 92 hours on their homework. (No, \( y = 92 \), not \( x = 92 \))

1. A student’s expected quiz score if they spent no time on their homework. (This is the y - intercept, 61, when \( x = 0 \))

So the correct meaning is: The number of hours a student should spend on their homework to expect a score of 92 on the quiz.

Answer:

The number of hours a student should spend on their homework to expect a score of 92 on the quiz.