Answer
The equation matches with the graph labeled as III.
Work Step by Step
$16x^2+25y^2=400$
$\frac{16x^2}{400}+\frac{25y^2}{400}=1$
$\frac{x^2}{25}+\frac{y^2}{16}=1$
$\frac{x^2}{5^2}+\frac{y^2}{4^2}=1$
$5\gt4$: major axis is horizontal.
Equation when major axis is horizontal:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
So,
$a^2=5^2$
$a=5$
Vertices: $(±a,0)=(±5,0)$
The equation matches with the graph labeled as III.