Question: how to find the distance between two slopes?
Answer: The distance between two points (x_1, y_1) and (x_2, y_2) can be defined as d= \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. Perpendicular lines are lines that intersect at a 90^{\circ} angle. The product of the slopes of two perpendicular lines is -1.