You can set the equations equal to each other and solve for x and then plug in that answer into either equation to get f(x).
So, f(x)=g(x)
3x-5=-4x+9
3x=-4x+14
7x=14
x=2
Now you plug x into the equations.
f(x)=3(2)-5 f(x)=6-5 f(x)=1
g(x)=-4(2)+9 g(x)=-8+9 g(x)=1
f(x) and g(x) are also equal to y.
So the point of intersection is (2,1).