12. In the Cartesian coordinate system $x O y$, if the line $y=k x+2$ is first translated 3 units upward along the $y$-axis, then 2 units to the right along the $x$-axis, and the final line coincides with the original line, then the value of the real number $k$ is ( )
(A) $\frac{3}{2}$
(B) $-\frac{3}{2}$
(C) $\frac{2}{3}$
(D) $-\frac{2}{3}$
Answer: (A)
Solution: The equation of the line obtained by first translating the line $y=k x+2$ 3 units upward along the $y$-axis is
$$
y=k x+5,
$$

then translating it 2 units to the right along the $x$-axis, the equation of the line becomes
$$
y=k(x-2)+5,
$$

since it is the same line as the original, we have $k(x-2)+5=k x+2$,

solving for $k$ gives
$$
k=\frac{3}{2} 。
$$