Given the points P(-1,1) and S(2,2), give the equation of the line passing through P and perpendicular to PS.

First, we can find the slope of the line PS, with the help of the formula m = (y₂- y₁)/(x₂- x₁) or if we substitute for the given points m_PS = (2 - 1)/(2 - (-1)) = (-1)/(3)= -1/3. Since the line l passing through P is perpendicular to PS, for l's slope m_l and PS's slope m_PS we know that m_PCm_l=-1. From 1/3 * m_l = -1 we can conclude that m_l = -3. Any line's equation can be represented in the form y = mx + b - so l's equation is y = -3x + b, and b = y + 3x. If we substitute (x,y) for the coordinates of P(-1,1), we will get b = 1 - 3 = -2. Finally, l's equation can be written as y = -3x -2 or 3x + y + 2 = 0.