The dy/dx=x²y²,
dy/y²=x²dx,
Integrating:
-1/y=x³/3+C.
Plug in (-3,1):
-1=-9+C, C=8, -1/y=x³/3+8,
y=-3/(x³+24). Note that x=∛-24=-2.8845 approx is an asymptote, and -3 is on one side of the asymptote while -2.8 is on the other side, so the linear approximation (tangent line at (-3,1)) is not going to help to get an approximation for y(-2.8).
At (-3,1), dy/dx=(-3)²(1)²=9.
So y-1=9(x+3) is the linear approximation.
That is, y=9x+28.
When x=-2.8, y=-25.2+28=2.8.
(Compare with y(-2.8): y=-3/(-21.952+24)=-1.465 approx.)
Because of the large discrepancy between the approximate and actual values, I think that the question contains at least one error. Should dy/dx=x²/y², for example?