To analyze the problem, let’s go through it step-by-step.

1. Observe the Lines: In the graph, we have two lines that appear to be parallel, indicating they likely have the same slope but may have different $y$-intercepts.

2. Slope and Intercept Analysis: Since the lines look parallel, they should have identical slopes. However, their $y$-intercepts are different, which means they are separated by a fixed vertical distance.

3. Translation Distance: The options mention translations by 3 or 9 units, so we should check how far apart the lines are in terms of vertical distance (which corresponds to translation if they’re parallel).

4. Correct Answer Evaluation:

   • Option A: States they have the same slopes but different $y$-intercepts, with a translation of 9 units.
   • Option B: Incorrect since it mentions different slopes.
   • Option C: Incorrect translation distance (3 units).
   • Option D: Also states different slopes, so it's incorrect.

Thus, Option A is correct, as it accurately states that the lines have the same slopes (parallel), different $y$-intercepts, and are translated by 9 units.

Would you like a more detailed explanation of how I determined the translation distance, or do you have further questions?

Related Questions

1. How do you determine the slope of a line from a graph?
2. What does it mean for two lines to be parallel on a coordinate plane?
3. How can you identify the $y$-intercept from a graph?
4. What is the significance of translation in geometry?
5. Why are translations described by distances (e.g., 3 units, 9 units) in such problems?

Tip

Parallel lines have identical slopes; any vertical distance between them represents the difference in their $y$-intercepts.