we can solve it by drawing of by algebra.
L: y=ax+b and a e (-2,+\infty)
the x-intercept of line L is b
1. -7=a*3+b ==> b=-3*a-7 b e (-\infty,-1) suff.
2. -9=a*5+b ==> b=-5*a-9 b e (-\infty,1) insuff.
I think C is correct
x-intercept of L is under control not only of b, but also a.
x= - b/a
1. x = (-3a -7)/a =-3 - 7/a, x-intercept wil (-) if a>0 and will (+) if -2<a<0 --> not sufficient
2. x = - 5 - 9/a --> not sufficient
1 and 2 combined: a = 1, b = - 13, so x - intercept negative --> suff.