Question

robert’s math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. what does the slope of the line represent? image of scatter plot with line of best fit answers: the change in a student’s actual quiz score for every additional one hour that student spent on their homework. the change in expected quiz score for every additional one hour students spend on their homework. a prediction of a student’s quiz score if they spent 1 hour on their homework. a student’s expected quiz score if they spent no time on their homework.

Explanation:

Step1: Recall slope interpretation

The slope of a line of best fit in a scatter plot (where \( y \)-axis is grade and \( x \)-axis is study hours) is \( \frac{\text{change in } y}{\text{change in } x} \), so it's the change in grade per unit change in study hours.

Step2: Analyze options

• "The change in a student’s actual quiz score for every additional one hour that student spent on their homework": Actual score is individual, but line of best fit is about expected (predicted) change. Eliminate.
• "The change in expected quiz score for every additional one hour students spend on their homework": Slope of line of best fit represents the predicted (expected) change in \( y \) (grade) for a 1 - unit change in \( x \) (study hours). This matches.
• "A prediction of a student’s quiz score if they spent 1 hour on their homework": This is the \( y \)-intercept or a specific prediction, not slope. Eliminate.
• "A student’s expected quiz score if they spent no time on their homework": This is the \( y \)-intercept, not slope. Eliminate.

Answer:

The change in expected quiz score for every additional one hour students spend on their homework