Find the slope of the line passing through the points \( (-7,-7) \) and \( (-3,6) \).

To find the slope of the line passing through the points \( (-7,-7) \) and \( (-3,6) \), you can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (-7, -7) \) and \( (x_2, y_2) = (-3, 6) \). Substituting in the values: \[ m = \frac{6 - (-7)}{-3 - (-7)} = \frac{6 + 7}{-3 + 7} = \frac{13}{4} \] So, the slope of the line is \( \frac{13}{4} \). --- Did you know that the concept of slope has been around for centuries? It was used as early as ancient civilizations for various mathematical and engineering projects! The Greeks and later mathematicians saw slope as vital in the study of geometry and astronomy, underscoring how foundational our understanding of it has remained in various fields. In real-world terms, understanding slope can be crucial for anything from constructing roads to designing buildings. If you're a cyclist, for instance, knowing the slope of a hill can help you gauge how much energy you will expend climbing it. Slope isn’t just a mathematical concept; it’s a practical tool that shapes our everyday experiences!