To find the new equation of the line after translating it one unit to the right and two units up, we start with the original equation:
\[ y = 3x + 2 \]
1. **Shifting the line one unit to the right**: To shift a line to the right, we replace \( x \) with \( x - 1 \). The equation becomes:
\[ y = 3(x - 1) + 2 \]
Simplifying this gives:
\[ y = 3x - 3 + 2 \]
\[ y = 3x - 1 \]
2. **Shifting the line two units up**: To shift a line up, we add 2 to the entire equation. The new equation becomes:
\[ y = (3x - 1) + 2 \]
\[ y = 3x + 1 \]
So, the equation of the new line after the translation is:
\[ y = 3x + 1 \]
The correct response is:
**y = 3x + 1**