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

Answer 1

To find the y-intercept of the line of fit, we can look at the provided points through which the line passes. The line of fit is said to pass through the points (0, 40) and (2, 70).

The y-intercept of a line is the point where the line crosses the y-axis, which corresponds to the value of \(y\) when \(x = 0\). In this case, from the coordinates (0, 40), we can see that the y-intercept is \(40\).

Now let's interpret this y-intercept in the context of the data:

The y-intercept of \(40\) indicates that if a student studies for \(0\) hours, they are predicted to earn a grade of \(40%\) on the test.

So the correct interpretation is:

40; a student who studies for 0 hours is predicted to earn 40% on the test.