To find the slope of the line that goes through the points (2, 27) and (13, 36), you can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
where \((x_1, y_1) = (2, 27)\) and \((x_2, y_2) = (13, 36)\).
Plugging in these values:
\[ m = \frac{36 - 27}{13 - 2} = \frac{9}{11} \]
Now, we can compare this with the options given:
- \( \frac{15}{163} \)
- \( \frac{11}{109} \)
- \( \frac{109}{11} \)
- \( \frac{163}{15} \)
The slope we calculated, \( \frac{9}{11} \), does not match any of those options. Let's check if we can convert \( \frac{9}{11} \) into a form that may be equivalent or simplify among the choices.
None of the choices match exactly as \( \frac{9}{11} \). However, it turns out the slope itself and the most straightforward way of stating it is \( \frac{9}{11} = 0.818\), which is not directly represented in the options.
Based on the calculation and given choices, none of the options provided represent the correct slope calculated from the mentioned points. If you are looking for the closest values or possible errors, please reconsider the options or re-check the plotted points.
So, in conclusion, the correct slope of the trend line based on the provided points is:
\[ \frac{9}{11} \] which does not correspond to any of the listed choices.