Anand'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, equals, 7, point, 2, x, plus, 55y=7.2x+55, where yy represents the expected quiz score and xx represents hours spent on homework that week. What is the meaning of the xx-value when y, equals, 77y=77?

Question

Answer
Multiple Choice Answers
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.

Answer 1

To find the meaning of the \(x\)-value when \(y = 77\) in the equation \(y = 7.2x + 55\), we first need to solve for \(x\).

Given: \[ 77 = 7.2x + 55 \]

Subtracting 55 from both sides: \[ 77 - 55 = 7.2x \] \[ 22 = 7.2x \]

Now, solve for \(x\) by dividing both sides by 7.2: \[ x = \frac{22}{7.2} \approx 3.06 \]

This means that when a student is expected to score 77 on the quiz, they should spend approximately 3.06 hours on homework.

Now, looking at the multiple-choice answers:

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

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