Question

question
claire’s math teacher finds that there’s 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 = 66 + 6.5x ), where ( y ) represents the expected quiz score and ( x ) represents hours spent on homework that week. what could the number 6.5 represent in the equation?
answer
a student’s expected quiz score if they spent 72.5 hours on their homework.
the change in expected quiz score for every additional one hour students spend on their homework.
how many hours a student spends studying all year.
a student’s expected quiz score if they spent no time on their homework.

Explanation:

Step1: Recall linear equation form

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept (initial value). Here, the equation is \(y=66 + 6.5x\), so \(m = 6.5\) and \(b = 66\).

Step2: Interpret the slope

In the context of the problem, \(y\) is the expected quiz score and \(x\) is the hours spent on homework. The slope \(m = 6.5\) represents the change in \(y\) (quiz score) for a unit change in \(x\) (homework hours). So, 6.5 represents the change in expected quiz score for every additional one hour students spend on their homework.

Answer:

The change in expected quiz score for every additional one hour students spend on their homework.