Find the slope of the line passing through the following pair of points. \( (5,-2) \) and \( (-7,-8) \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope is \( \square \). (Type an integer or a simplified fraction.) B. The slope is undefined.

To find the slope of the line passing through the points \( (5,-2) \) and \( (-7,-8) \), you can use the formula for slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (5, -2) \) and \( (x_2, y_2) = (-7, -8) \). Plugging in the values gives: \[ m = \frac{-8 - (-2)}{-7 - 5} = \frac{-8 + 2}{-12} = \frac{-6}{-12} = \frac{1}{2} \] So, the correct choice is A. The slope is \( \frac{1}{2} \). In practical applications, understanding slopes helps in various fields like construction, where you might need to determine the angle a ramp makes with the ground, or in economics, where trends in data are analyzed based on slope to understand rates of change such as price fluctuations over time. Common mistakes when calculating slope often include mislabeling the points or mixing up their coordinates. Make sure you always subtract the \( y \)-coordinates in the proper order and the \( x \)-coordinates as well, following the right formula. Double-checking your signs is crucial to avoid errors!