Question

question: tociqs 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? answer: 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 student spent on their homework. a prediction of a student’s quiz score if they spent x hours on homework. the change in a student’s actual quiz score for every additional one hour that student spent on their homework.

Explanation:

Step1: Understand Line of Best Fit Slope

The line of best fit in a scatter plot (here, study hours vs quiz grades) has a slope that represents the rate of change. The slope formula is $m = \frac{\Delta y}{\Delta x}$, where $\Delta y$ is change in y (quiz grades) and $\Delta x$ is change in x (study hours).

Step2: Interpret the Slope's Meaning

The slope of the line of best fit shows the predicted change in quiz grade (y - variable) for each additional hour (x - variable) spent studying. It's a prediction (not actual for each student, since points are scattered) of how much the grade is expected to change per extra study hour. The options about "actual" grades are incorrect because the line is a model (prediction), and the y - intercept is for 0 study hours, not the slope. So the slope represents the change in expected (predicted) quiz score for every additional one - hour studied.

Answer:

The change in expected quiz score for every additional one hour student spent on their homework. (Or matching the option: "The change in expected quiz score for every additional one hour student spent on their homework" among the given options, likely the second option in the list related to expected change per hour studied)