Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.

Question

scatter plot titled students' data, with points plotted at 1 comma 60, 2 comma 60, 2 comma 70, 2 comma 80, 3 comma 80, 3 comma 90, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 40 and 2 comma 70

Find the slope of the line of fit and explain its meaning in the context of the data.
15; for each additional hour a student studies, their grade is predicted to increase by 15% on the test
30; for each additional hour a student studies, their grade is predicted to increase by 30% on the test
40; a student who studies for 0 hours is predicted to earn 40% on the test
70; a student who studies for 0 hours is predicted to earn 70% on the test

Answer 1

To find the slope of the line of fit represented by the points (0, 40) and (2, 70), we can use the slope formula:

\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

Here, \((x_1, y_1) = (0, 40)\) and \((x_2, y_2) = (2, 70)\).

Plugging in these values:

\[ m = \frac{70 - 40}{2 - 0} = \frac{30}{2} = 15 \]

The slope of the line of fit is 15.

Meaning in Context:

In the context of the data, the slope indicates that for each additional hour a student studies, their grade on the test is predicted to increase by 15%. This means that increased study time correlates with higher grades, providing a useful insight for students about the impact of their study habits on academic performance.

Thus, the correct interpretation from your choices is:

15; for each additional hour a student studies, their grade is predicted to increase by 15% on the test.