Let x=0 get y=3, so q (0,3)

Because point q and point p are symmetrical about x,

So P(0, -3)

Because the linear function y=kx+b, the image passes through the point (-2,5) and intersects with the Y axis at point P.

So 5 =-2k+b,-3 = 0 * k+b.

The solution is k =-4 and b =-3.

So the analytical formula is y=-4x-3.