Transport equation data on a line

Let $u : \mathbb{R}^{2} \to \mathbb{R}$ solve $\partial_{x}u + 2\partial_yu = 0$ on $\mathbb{R}^{2}$ with u(x, y) = sin x on the line y = 3x + 1, and let $v : \mathbb{R}^{2} \to \mathbb{R}$ solve $\partial_{x}v + 2\partial_yv = 0$ with v(x, 0) = sin x. Let S = [0,1] × [0,1]. Which of the following statements are true?