Question

question
chase’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 = 7x + 64 ), where ( y ) represents the expected quiz score and ( x ) represents hours spent on homework that week. what is the meaning of the ( y )-value when ( x = 1 )?
answer
a student’s expected quiz score if they spent 1 hour on their homework.
a student’s expected quiz score if they spent 71 hours on their homework.
how many hours a student spends studying all year.
the change in expected quiz score for every additional one hour students spend on their homework.
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Explanation:

Step1: Understand the equation

The equation is \( y = 7x + 64 \), where \( y \) is the expected quiz score and \( x \) is the hours spent on homework per week. We need to find the meaning of \( y \) when \( x = 1 \).

Step2: Substitute \( x = 1 \) into the equation

Substitute \( x = 1 \) into \( y = 7x + 64 \). So, \( y = 7(1) + 64 = 7 + 64 = 71 \). Now, interpret what \( x = 1 \) means: \( x = 1 \) means a student spends 1 hour on homework per week. Then \( y = 71 \) is the expected quiz score for that student. So we check the options:

• Option 1: "A student’s expected quiz score if they spent 1 hour on their homework." This matches because \( x = 1 \) (1 hour homework) gives \( y = 71 \) (expected quiz score).
• Option 2: "A student’s expected quiz score if they spent 71 hours on their homework." \( x = 71 \) would be needed for this, not \( x = 1 \), so incorrect.
• Option 3: "How many hours a student spends studying all year." The equation is about weekly homework and weekly quiz scores, not all - year study, so incorrect.
• Option 4: "The change in expected quiz score for every additional one hour students spend on their homework." This is the meaning of the slope (7), not the meaning of \( y \) when \( x = 1 \), so incorrect.

Answer:

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