Question

The graph below shows the hours students spent studying and their science test scores.

Hours Spent Studying vs. Science Test Scores
A graph has hours spent studying on the x-axis and test score on the y-axis. A line has a regression equation of y = 3.1 x + 40.5.

A student gets a score of 70 on the test. Based on the trend line in the scatter plot, how much time did the student spend studying?
3.1 hours
4.5 hours
9.5 hours
40.5 hours

Answer 1

(c) 9.5 hours

Explanation:

The equation of the trend line predicts a score based on study hours. Here, we're asked for the inverse relation: finding a number of study hours based on a given score.

Inverse relation

We can solve the equation for x in terms of y:

y = 3.1x +40.5

y -40.5 = 3.1x . . . . subtract 40.5

(y -40.5)/3.1 = x . . . . divide by the coefficient of x

This tells us the number of hours spent studying for a particular score.

Application

Using y=70, we find the number of study hours to be ...

x = (70 -40.5)/3.1 = 29.5/3.1 ≈ 9.516 ≈ 9.5

The student spent about 9.5 hours studying.