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 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80

Determine the equation of the line of fit.
y = 5x + 60
y = 5x + 80
y = 10x + 60
y = 10x + 80

Answer 1

To determine the equation of the line of fit based on the points provided (0, 60) and (2, 80), we first need to calculate the slope of the line.

The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Using the points (0, 60) and (2, 80):

• \((x_1, y_1) = (0, 60)\)
• \((x_2, y_2) = (2, 80)\)

Now, plug the values into the slope formula:

\[ m = \frac{80 - 60}{2 - 0} = \frac{20}{2} = 10 \]

Now that we have the slope (m = 10), we can use the point-slope form of a line to form the equation. The point-slope form is:

\[ y - y_1 = m(x - x_1) \]

We can use one of our points; let's use (0, 60):

\[ y - 60 = 10(x - 0) \]

This simplifies to:

\[ y - 60 = 10x \] \[ y = 10x + 60 \]

Thus, the equation of the line of fit is:

\[ \boxed{y = 10x + 60} \]