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 the x-axis labeled study time in hours and the y-axis labeled grade percent. Points are plotted at 1 comma 65, 2 comma 60, 2 comma 70, 2 comma 80, 3 comma 70, 3 comma 90, 4 comma 85, and 4 comma 90, and a line of fit drawn passing through the points 0 comma 50 and 2 comma 70

Determine the equation of the line of fit.
y = 5x + 50
y = 5x + 70
y = 10x + 50
y = 10x + 70

Answer 1

To determine the equation of the line of fit, we can identify two points that the line passes through and use the slope-intercept form \( y = mx + b \).

From the plot description, we have the points:

1. (0, 50)
2. (2, 70)

First, we calculate the slope \( m \) of the line using the formula:

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

Substituting our points (0, 50) and (2, 70):

\[ m = \frac{70 - 50}{2 - 0} = \frac{20}{2} = 10 \]

Now that we have the slope \( m = 10 \), we can use one of the points to find the y-intercept \( b \). Using the point (0, 50):

\[ y = mx + b \implies 50 = 10(0) + b \implies b = 50 \]

Thus, the equation of the line of fit is:

\[ y = 10x + 50 \]

So, the correct answer is:

y = 10x + 50