Let the equation of the line be y=mx+b.
The y-intercept is b and the x-intercept is -b/m, so b-b/m=9 therefore m=b/(b-9).
Also, plugging in (2,2): 2=2m+b=2b/(b-9)+b by substituting for m.
Multiply through by b-9: 2(b-9)=2b+b(b-9).
So 2b-18=2b+b²-9b, b²-9b+18=0=(b-6)(b-3). So we have two possible values for b=3, 6 and the corresponding values of m are 3/(3-9)=-1/2 and 6/(6-9)=-2.
So there are two lines fulfilling the given conditions:
y=-x/2+3 (y-int = 3, x-int = 6) and y=-2x+6 (y-int = 6, x-int = 3), so sum of intercepts is 9. And both lines pass through A(2,2), which is where the two lines intersect each other.