(1) If two functions are symmetric about the origin and about y=x, then these two functions are inverse functions. From ax+3y-9=0, Y=-a/3X+3 is solved, and its inverse function is X=-a/3Y+3. Compared with X=3Y-b, A =-9.

(2) Set the intercept formula of the straight line, x/a+y/b =1(a >; 0, b>0), substitute (1, 3), 1/a+3/b= 1, ab=2*6, so that a=2.

b=6，

So the linear equation: 3x+y-6=0.