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 )? a students expected quiz score if they spent 89 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 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: Analyze the equation

The equation \(y = 56+8.2x\) is in the form \(y = mx + b\) (slope - intercept form of a linear equation), where \(y\) is the dependent variable (quiz score), \(x\) is the independent variable (hours of homework), \(m = 8.2\) (slope) and \(b=56\) (y - intercept).

Step2: Substitute \(y = 89\) into the equation

When \(y = 89\), we have the equation \(89=56 + 8.2x\). We solve for \(x\) to find the value of \(x\) when \(y = 89\).

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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.