Find the slope of the line that passes through \( (2,7) \) and \( (5,5) \). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

To find the slope of the line that passes through the points \( (2,7) \) and \( (5,5) \), we use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points \( (x_1, y_1) = (2, 7) \) and \( (x_2, y_2) = (5, 5) \): \[ m = \frac{5 - 7}{5 - 2} = \frac{-2}{3} \] So, the slope of the line is \( -\frac{2}{3} \). --- Did you know that the concept of slope originated long before algebra as we know it? Ancient civilizations, including the Greeks, were fascinated by triangles and angles, which laid the groundwork for understanding linear relationships. The slope represents how steep a line is, and it’s a key concept in fields like physics and engineering! Slope isn't just a math concept; it has real-world applications everywhere! For example, in construction, understanding slope is crucial for designing ramps or roofs that drain water effectively. A slope of \( -\frac{2}{3} \) in architectural terms could translate to a specific angle for a staircase or pathway, allowing for smooth transitions and safety in design.