A straight line L with negative slope passes through the point (8, 2) and intersects the positive coordinate axes at points P and Q. As L varies the absolute minimum value of OP + OQ is (O is origin).

The equation of the line is (y – 2) = m(x – 8), m < 0The coordinates of P and Q are P8-2m,0  and  Q(0, 2-8m)Therefore, OP+OQ=8-2m+2-8m=10+2-m+8(-m)≥10+22-m×8(-m)=18Thus, absolute minimum value of OP + OQ = 18.