Question

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. the change in expected quiz score for every additional one hour students spend on their homework. a students expected quiz score if they spent 98 hours on their homework. a students expected quiz score if they spent 1 hour on their homework.

Explanation:

Step1: Substitute \( y = 98 \) into the equation

Given the equation \( y=8x + 57 \), when \( y = 98 \), we have \( 98=8x + 57 \).

Step2: Solve for \( x \)

Subtract 57 from both sides: \( 98−57=8x \), so \( 41 = 8x \). Then divide both sides by 8: \( x=\frac{41}{8}=5.125 \). This \( x \) - value represents the number of hours a student should spend on their homework to expect a score of 98.

Answer:

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