\( 1 \leftarrow \begin{array}{l}\text { Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether } \\ \text { the line through the points rises, falls, is horizontal, or is vertical. } \\ (-3,6) \text { and }(6,5) \\ \text { Select the correct choice below and, if necessary, fill in the answer box within your choice. } \\ \text { A. The slope is } \frac{9}{-1} \text {. (Simplify your answer.) } \\ \text { B. The slope is undefined. }\end{array} \).

To find the slope of the line passing through the points \((-3, 6)\) and \((6, 5)\), we can use the formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, we have: - \(x_1 = -3\), \(y_1 = 6\) - \(x_2 = 6\), \(y_2 = 5\) Now, we can substitute these values into the slope formula: \[ m = \frac{5 - 6}{6 - (-3)} \] Calculating the numerator and denominator: 1. **Numerator**: \(5 - 6 = -1\) 2. **Denominator**: \(6 - (-3) = 6 + 3 = 9\) Now substituting these values back into the slope formula: \[ m = \frac{-1}{9} \] This means the slope of the line is \(-\frac{1}{9}\). Next, we can determine the behavior of the line: - Since the slope is negative, the line falls as it moves from left to right. Thus, the final answer is: - The slope is \(-\frac{1}{9}\) (which simplifies to \(-\frac{1}{9}\)). - The line falls. So, the correct choice is: **A. The slope is \(-\frac{1}{9}\). The line falls.**