To find the new points on the translated line, we first need to apply the translations to the original points \((-4, 2)\) and \((-4, 6)\).
Step 1: Translate each point.
- Translation: 3 units to the right means we add 3 to the x-coordinate.
- Translation: 2 units down means we subtract 2 from the y-coordinate.
For the point \((-4, 2)\):
- New x-coordinate: \(-4 + 3 = -1\)
- New y-coordinate: \(2 - 2 = 0\)
- New point: \((-1, 0)\)
For the point \((-4, 6)\):
- New x-coordinate: \(-4 + 3 = -1\)
- New y-coordinate: \(6 - 2 = 4\)
- New point: \((-1, 4)\)
Step 2: Compile the new points. The new points on the translated line are: \[ (-1, 0) \quad \text{and} \quad (-1, 4) \]