What is the slope of the line through \( (-7,-2) \) and \( (-6,7) \) ? Choose 1 answer: (A) \( \frac{1}{9} \) (B) 9 (C) -9 (D) \( -\frac{1}{9} \) (B)

To find the slope of the line through two points, you can use the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in our points \( (-7,-2) \) and \( (-6,7) \), we have \( y_1 = -2 \), \( y_2 = 7 \), \( x_1 = -7 \), and \( x_2 = -6 \). So, the slope is: \[ \frac{7 - (-2)}{-6 - (-7)} = \frac{7 + 2}{-6 + 7} = \frac{9}{1} = 9. \] Thus, the correct answer is (B) 9! And don't forget the importance of visualization! Picture this: a straight line on a graph that steeply rises as you move from left to right, just like a roller coaster climbing up towards the sky. That's the representation of a positive slope! For a fun twist in slope problems, imagine this situation as a treasure map! Each point is a clue, and finding the slope helps you determine the steepness of your treasure trail. Just remember to watch for signs of tricks—like flipping signs, especially when subtracting negatives!