A rectangle in the coordinate plane is shown below. A line with slope $\frac{1}{3}$ splits this rectangle into two regions with equal area. What is the $y$-intercept of this line?

[asy]
unitsize(1.2 cm);

pair A, B, C, D;

A = (0,2);
B = (0,0);
C = (3,0);
D = (3,2);

draw(A--B--C--D--cycle);

label("$(-2,3)$", A, NW);
label("$(-2,-5)$", B, SW);
label("$(4,-5)$", C, SE);
label("$(4,3)$", D, NE);
[/asy]