Question

zendayas 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 = 7.6x + 60 ), 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 = 100 )?
answer
the number of hours a student should spend on their homework to expect a score of 100 on the quiz.
a students expected quiz score if they spent no time on their homework.
a students expected quiz score if they spent 100 hours on their homework.
the change in expected quiz score for every additional one hour students spend on their homework.

Explanation:

Step1: Analyze the linear equation

The given linear equation is \( y = 7.6x+60\), where \(y\) is the expected quiz score and \(x\) is the hours spent on homework.

Step2: Recall the slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the equation \(y = 7.6x + 60\), the slope \(m = 7.6\).
The slope \(m=\frac{\Delta y}{\Delta x}\), which represents the change in \(y\) (quiz score) for a unit change in \(x\) (homework hours).

Answer:

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