Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. \( (2,7) \) and \( (-6,-9) \) Select the correct choice below and fill in the answer box within your choice. A. The slope is \( \square \). (Simplify your answer.) B. The slope is undefined.

To find the slope of the line passing through the points \( (2,7) \) and \( (-6,-9) \), we can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \( (x_1, y_1) = (2, 7) \) and \( (x_2, y_2) = (-6, -9) \). Now, let's substitute the values into the formula: 1. Calculate \( y_2 - y_1 \): \[ y_2 - y_1 = -9 - 7 = -16 \] 2. Calculate \( x_2 - x_1 \): \[ x_2 - x_1 = -6 - 2 = -8 \] 3. Now, substitute these results into the slope formula: \[ m = \frac{-16}{-8} \] 4. Simplify the fraction: \[ m = 2 \] Now that we have the slope, we can determine the behavior of the line: - Since the slope \( m = 2 \) is positive, the line rises. Thus, the correct choice is: A. The slope is \( 2 \). (Simplify your answer.)