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 80, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 90, and 4 comma 98, and a line of fit drawn passing through the points 0 comma 70 and 1 comma 75

Determine the equation of the line of fit.

y = 5x + 70
y = 5x + 80
y = 10x + 70
y = 10x + 80

Answer 1

To determine the equation of the line of fit that passes through the points (0, 70) and (1, 75), we can use the slope-intercept form of a linear equation, which is:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

1. Find the slope (m): The slope is calculated as:

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

Using the points (0, 70) and (1, 75):

\[ m = \frac{75 - 70}{1 - 0} = \frac{5}{1} = 5 \]

2. Using one of the points to find the y-intercept (b): We can use the point (0, 70) to find \( b \):

\[ y = 5x + b \]

Substituting \( x = 0 \) and \( y = 70 \):

\[ 70 = 5(0) + b \implies b = 70 \]

Thus, the equation of the line of fit is:

\[ y = 5x + 70 \]

Therefore, the correct choice is:

\[ y = 5x + 70 \]