Let the expression of the function be y=k*x+b, where k and b are to be determined.

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).