To determine the slope of a line intersecting the points (2, 2) and (6, 7), the formula used is (y2 - y1) / (x2 - x1). Substituting the coordinates, the slope is calculated as (7 - 2) / (6 - 2), which simplifies to 5 / 4. This indicates that for every 4 units moved horizontally, the line rises 5 units vertically. The discussion emphasizes the importance of showing effort in problem-solving, particularly for students seeking help. Understanding how to calculate slope is fundamental in geometry and algebra.