Substituting (3,5) and (-4,9), there are
5=3k+b - ( 1)
-9=-4k+b - (2)
(1)-(2), 14=7k, so k=2.
Substituting (1), 5=6+b, that is, b=- 1.
The expression of the function is y=2x- 1.
Find the intersection with the y axis, let x=0, and get y=- 1.
That is, the coordinates of the intersection point are (0,-1).