Answer: (C) $x - 3y = 7$
The given line $2x - 6y = 7$ has slope $\frac{1}{3}$. Option C, $x - 3y = 7$, has the same slope $\frac{1}{3}$ but different constant, so the lines are parallel.
For parallel lines: $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$.
Rewrite $2x - 6y = 7$ as $x - 3y = \frac{7}{2}$. Check each option for same ratio of coefficients of x and y but different constant ratio. Only option C gives $\frac{1}{1} = \frac{-3}{-3}$ (same slope) but $\frac{7/2}{7} \neq 1$ (different constant) — confirming parallel lines. Option D ($x = \frac{7}{2} - 3y \Rightarrow x + 3y = \frac{7}{2}$) has a different slope entirely.