Slope m has a form of,
[tex]m=\dfrac{\Delta{y}}{\Delta{x}}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have points A and B,
[tex]A(x_1,y_1),B(x_2,y_2)\longrightarrow A(-4,5),B(2,-3)[/tex]
Now insert the values in the slope formula,
[tex]m=\dfrac{-3-5}{2-(-4)}=\dfrac{-8}{6}=\boxed{-\dfrac{4}{3}}[/tex]
The answer is A.
Hope this helps.
r3t40