The graphs of a circle and a linear equation are shown. The circle is centered at the origin and passes through $(5,0)$, and the line passes through $(-4,-3)$ and $(3,4)$. What is the product of the y-coordinates of all solutions $(x,y)$ to this system?

(Assume a graph is provided showing the circle $x^2+y^2=25$ and the line $y=x+1$ intersecting at $(-4,-3)$ and $(3,4)$.)