Question

anand’s 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 = 7.2x + 55 ), 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 = 77 )?

answer

the number of hours a student should spend on their homework to expect a score of 77 on the quiz.
a student’s expected quiz score if they spent 77 hours on their homework.
the change in expected quiz score for every additional one hour students spend on their homework.
a student’s expected quiz score if they spent no time on their homework.

Explanation:

Step1: Understand the variables

In the equation \( y = 7.2x + 55 \), \( y \) is the expected quiz score and \( x \) is the hours spent on homework. We need to find the meaning of \( x \) when \( y = 77 \).

Step2: Analyze each option

• Option 1: "The number of hours a student should spend on their homework to expect a score of 77 on the quiz." This makes sense because we are solving for \( x \) (hours) when \( y \) (score) is 77.
• Option 2: "A student’s expected quiz score if they spent 77 hours on their homework." Here, \( x \) would be 77, but we are finding \( x \) when \( y = 77 \), so this is incorrect.
• Option 3: "The change in expected quiz score for every additional one hour students spend on their homework." This describes the slope (7.2), not the meaning of \( x \) when \( y = 77 \), so incorrect.
• Option 4: "A student’s expected quiz score if they spent no time on their homework." This is the y - intercept (55), not related to \( y = 77 \), so incorrect.

Answer:

The number of hours a student should spend on their homework to expect a score of 77 on the quiz.