The problem statement, all variables and given/known data A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes at points P and Q. As L varies, what is the absolute minimum value of OP + OQ? The attempt at a solution Let x and y be two points on the line. Using the slope point formula, we have (y-2) = m(x-8). Writing this in intercept form, one gets x/(8 - 2/m) + y/(2 - 8m) = 1. This implies coordinates of P and Q are (8 - 2/m, 0) and (0, 2 - 8m) respectively. ∴ OP + OQ = 10 + (-2/m - 8/m) I can't figure out how to proceed from there. How do you find out the minimum value for the last term?