Question: Find the coordinates of the image of Jā²(-5, -1) after the translation $ (x, y) \to (x - 2, y) $.
1. **State the problem:** We need to find the new coordinates of point $J'(-5, -1)$ after applying the translation rule $ (x, y) \to (x - 2, y) $.
2. **Understand the translation:** The translation moves every point 2 units to the left (subtracting 2 from the $x$-coordinate) and leaves the $y$-coordinate unchanged.
3. **Apply the translation:**
- Original $x$-coordinate: $-5$
- New $x$-coordinate: $$-5 - 2 = -7$$
- Original $y$-coordinate: $-1$
- New $y$-coordinate: $$-1$$
4. **Write the new coordinates:** The image of $J'$ after translation is $$(-7, -1)$$.
5. **Check the options:** The correct choice is D. $(-7, -1)$.
**Final answer:** $\boxed{(-7, -1)}$