Carlos'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, 61, plus, 7, point, 6, xy=61+7.6x, 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, 92y=92?

Question

Answer
Multiple Choice Answers
The number of hours a student should spend on their homework to expect a score of 92 on the quiz.
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 92 hours 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 \( y = 92 \), we can use the equation \( y = 61 + 7.6x \) and set \( y \) to 92:

\[ 92 = 61 + 7.6x \]

Now, solve for \( x \):

1. Subtract 61 from both sides: \[ 92 - 61 = 7.6x \] \[ 31 = 7.6x \]

2. Divide both sides by 7.6: \[ x = \frac{31}{7.6} \] \[ x \approx 4.07 \]

So, when the quiz score \( y \) is 92, the corresponding value of \( x \) is approximately 4.07 hours.

This means that a student should spend about 4.07 hours on their homework to expect a quiz score of 92.

The correct answer is: The number of hours a student should spend on their homework to expect a score of 92 on the quiz.