What is a and b if ax+by=0 passes through the points (9,8) and (8,9)

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).