To determine the equation of the line of best fit based on the data points (2009, 1330) and (2013, 1492), we can first find the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Where:
- \( (x_1, y_1) = (2009, 1330) \)
- \( (x_2, y_2) = (2013, 1492) \)
Plugging in the values:
\[ m = \frac{1492 - 1330}{2013 - 2009} = \frac{162}{4} = 40.5 \]
Now that we have the slope, we can use the point-slope form of the linear equation to find the equation of the line. The point-slope form is:
\[ y - y_1 = m(x - x_1) \]
Using one of the points, we can choose (2009, 1330):
\[ y - 1330 = 40.5(x - 2009) \]
Expanding this, we get:
\[ y - 1330 = 40.5x - 81364.5 \]
Adding 1330 to both sides gives us:
\[ y = 40.5x - 80034.5 \]
Now we can compare this with the provided options.
To reformat it in the linear form \( y = mx + b \):
- Find the y-intercept. We already have:
\[ b = -80034.5 \]
This rewriting might not match any standard fraction format provided directly, as they seem to have different constants.
- Checking these fractions, they are expressed in terms of units around 81 and divided forms.
It seems like you might want a direct choice without further calculation refinement or another plot straight away. However, based on the slope we found, you may want to enter or select the best-suited answer from the next available, but you would need better clarity on their coefficient structures to derive completely or best-fit focus. Checking those against slope intercepts accordingly.
If you have any additional conditions or contexts needed with adjusting against a total trend that estimates over the scatter, let me know!