Equivalence relation with ordered pair of integers excluding zero.

Question

Let $(x,y)$ be an ordered pair of integers excluding zero. Two ordered pairs $(x_1, y_1)$ and $(x_2, y_2)$ are equivalent if $x_1y_2 = x_2y_1$. Is this an equivalence relation? Prove or disprove.

Answer 1

HINT

$x_1y_2=x_2y_1$ iff $\frac{x_1}{x_2} = \frac{y_1}{y_2}$

HINT 2 (thanks @hardmath)

$x_1y_2=x_2y_1$ iff $\frac{x_1}{y_1} = \frac{x_2}{y_2}$