To determine if two lines are perpendicular algebraically, one method is to find the slopes of the lines; if the product of the slopes equals -1, the lines are perpendicular. Another approach involves forming unit vectors from the lines' direction components and calculating their inner product; if the result is zero, the lines are also perpendicular. Both methods provide a reliable way to assess perpendicularity without graphing. Understanding these algebraic techniques can enhance problem-solving skills in geometry. Mastering these concepts is essential for success in algebra and geometry courses.