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 number of hours a student should spend on their homework to expect a score of 89 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 no time on their homework. a students expected quiz score if they spent 89 hours on their homework.

Explanation:

In the given linear equation \(y = 56+8.2x\), \(y\) is the dependent variable (quiz score) and \(x\) is the independent variable (hours of homework). When we set \(y = 89\) and solve for \(x\), we are finding the value of \(x\) (hours of homework) that corresponds to the value of \(y = 89\) (quiz score).

The second option refers to the slope (\(8.2\) in the equation \(y=mx + b\), where \(m\) is the slope). The third option refers to the \(y\) - intercept (\(b = 56\) in \(y=mx + b\)). The fourth option misinterprets the roles of \(x\) and \(y\) in the equation.

Answer:

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