Question

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.

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 determine the slope of the line of fit from the provided points, we can analyze the coordinates of two points that lie on the line of fit, which are given as (0, 40) and (2, 70).

The slope \( m \) of a line given two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the coordinates of the points:

- \( (x_1, y_1) = (0, 40) \)
- \( (x_2, y_2) = (2, 70) \)

Now substituting into the slope formula:

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

The slope of the line of fit is 15.

### Meaning of the Slope in Context

The slope of 15 indicates that for each additional hour a student studies, their grade is predicted to increase by 15% on the test.

Thus, the correct interpretation from the options provided is:

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