What is a and b if ax+by=0 passes through the points (9,8) and (8,9) Solution ax+by = 0 passes through (9,8) and (8,9). Therefore the coordinates of the points (9,8) and (8,9) should satisfy the equation ax+by = 0. (9,8) : a*9+b*8 = 0...........(1) (8,9): a*8+b*9 = 0...........(2) Add the equations (1) and (2): 17(a+b) = 0 Or a+b = 0 Also eq(2) - eq(1) gives: a-b = 0. So a+b =0 and a-b = 0. Adding 2a = 0. Or a = 0 Subracting 2b = 0. Or b =0. So there is no line like ax+by = 0 passes through (9,8) and (8,9). The line passing through Two points: The line passing through 2 points (x1,y1) and (x2,y2) is : y-y1 = {(y2-y1)/(x2-x1)}(x-x1). Put (x1,y1) = (9,8) and (x2,y2)= (8,9). y-8 = {(9-8)/(8-9)}(x-9) y-8 = -1(x-9) x+y = 1. Therefore the line passing through (9,8) and (8,9) is : x+y = 1 making intercepts 1 and 1 on x and y axis respectively and this line cannot be reduced to the form ax+by = 0 which is a line through origin (making zero intercepts on x and y axis)..