To find the equations of the asymptotes of the hyperbola defined by the equation x^2/25 - y/16 = 1, we can consider the standard form equation of a hyperbola centered at the origin:
(x^2/a^2) - (y^2/b^2) = 1
Comparing this with the given equation, we have a^2 = 25 and b^2 = 16. Taking the square root of both sides, we get a = 5 and b = 4.
The general equations for the asymptotes of a hyperbola centered at the origin are y = ±(b/a)x.
Substituting the values of a and b, we have the equations for the asymptotes:
y = ±(4/5)x
Therefore, the equations of the asymptotes of the given hyperbola are y = (4/5)x and y = -(4/5)x.