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, 7, point, 3, x, plus, 61y=7.3x+61, where yy represents the expected quiz score and xx represents hours spent on homework that week. What is the meaning of the yy-value when x, equals, 1x=1?

Question

Answer
Multiple Choice Answers
A student's expected quiz score if they spent no time 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 1 hour on their homework.
How many hours a student spends studying all year.

Answer 1

To find the meaning of the \( y \)-value when \( x = 1 \) in the equation \( y = 7.3x + 61 \), we need to substitute \( x = 1 \) into the equation.

Substituting \( x = 1 \):

\[ y = 7.3(1) + 61 = 7.3 + 61 = 68.3 \]

The \( y \)-value when \( x = 1 \) is 68.3. This means that if a student spends 1 hour on their homework, their expected quiz score is 68.3.

Looking at the multiple choice answers:

1. A student's expected quiz score if they spent no time on their homework. (This would correspond to \( x = 0 \).)
2. The change in expected quiz score for every additional one hour students spend on their homework. (This refers to the slope of the line, which is 7.3.)
3. A student's expected quiz score if they spent 1 hour on their homework. (This is correct since we just calculated that it equals 68.3 when \( x = 1 \).)
4. How many hours a student spends studying all year. (This does not relate to the equation.)

Therefore, the correct answer is:

A student's expected quiz score if they spent 1 hour on their homework.