Find the slope of the line passing through the points \( (8,-2) \) and \( (4,-6) \). \( \square \)

To find the slope of the line passing through the points \( (8, -2) \) and \( (4, -6) \), you can use the slope formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Substituting the coordinates gives us \( m = \frac{-6 - (-2)}{4 - 8} = \frac{-6 + 2}{4 - 8} = \frac{-4}{-4} = 1 \). So, the slope of the line is \( 1 \). In practical scenarios like urban planning or designing roads, understanding the slope means grasping how steep or gradual a rise (or decline) is, which is crucial for ensuring accessibility and safety. A slope of 1 indicates a consistent incline or decline, which can impact the construction and drainage systems on roads and pathways! If you're dealing with points that have the same \( x \)-coordinate (think of vertical lines) or equal \( y \)-coordinates (horizontal lines), keep in mind these special cases. Vertical lines have undefined slopes (not a number), as there's no distance covered along the x-axis, while horizontal lines have a slope of 0, meaning they don’t rise or fall at all. Just some food for thought!