\( \left. \begin{array} { l } { \frac { m = y _ { 2 } - y _ { 1 } } { x _ { 2 } - x _ { 1 } } } \\ { ( - 3,4 ) \quad ( 6 , - 2 ) } \\ { x _ { 1 } , y _ { 1 } \quad x _ { 2 } , y _ { 2 } } \end{array} \right. \)

To find the slope \( m \) of the line passing through the points \( (-3, 4) \) and \( (6, -2) \), plug the coordinates into the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1 = -3, y_1 = 4, x_2 = 6, y_2 = -2 \). Thus, \( m = \frac{-2 - 4}{6 - (-3)} = \frac{-6}{9} = -\frac{2}{3} \). Slope can be visualized as the steepness of a line. In real-world terms, think of it as how fast you're going downhill or uphill on a road! A slope of \(-\frac{2}{3}\) means for every 3 units you move horizontally to the right, you go down 2 units. It's like a gentle slope, perfect for leisurely hikes.