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

Answer 1

Answer: The y-intercept of the line of fit can be found by looking at the point where the line crosses the y-axis. From the given information, we know that the line passes through the points (0, 40) and (2, 70). To find the equation of the line, we can use the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept. We can find the slope of the line by using the two points:

m = (y2 - y1) / (x2 - x1)

m = (70 - 40) / (2 - 0)

m = 30

So the equation of the line is:

y = 30x + b

To find the y-intercept, we can plug in one of the points and solve for b. Let's use the point (0, 40):

40 = 30(0) + b

b = 40

Therefore, the y-intercept of the line of fit is 40. In the context of the data, this means that a student who did not study at all (0 hours) is predicted to earn a grade of 40 on the test. However, it's important to note that this prediction is based on the data collected from the sample of 8 students and the line of fit may not accurately predict the grades of all students who did not study.

Your welcome.