Question

arturos 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 = 56 + 8.2x ) 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 = 89 )?
the change in expected quiz score for every additional one hour students spend on their homework.
a students expected quiz score if they spent 89 hours on their homework.
a students expected quiz score if they spent no time on their homework.
the number of hours a student should spend on their homework to expect a score of 89 on the quiz.

Explanation:

Step1: Substitute \( y = 89 \) into the equation

Given the equation \( y=56 + 8.2x \), when \( y = 89 \), we have \( 89=56 + 8.2x \).

Step2: Solve for \( x \)

Subtract 56 from both sides: \( 89-56=8.2x \), so \( 33 = 8.2x \). Then \( x=\frac{33}{8.2}\approx4.02 \). This \( x \)-value represents the number of hours a student should spend on their homework to expect a score of 89 on the quiz.

Answer:

The number of hours a student should spend on their homework to expect a score of 89 on the quiz.