To translate the line given by the equation \(y = 3x + 2\) one unit to the right and two units up, we need to adjust the equation accordingly.
Step 1: Shift the line one unit to the right.
- To shift a line one unit to the right, we replace \(x\) with \(x - 1\).
- The equation becomes: \[ y = 3(x - 1) + 2 \]
- Simplifying this: \[ y = 3x - 3 + 2 \] \[ y = 3x - 1 \]
Step 2: Shift the line two units up.
- To shift the line two units up, we add 2 to the entire equation. So we take the current equation \(y = 3x - 1\) and add 2: \[ y = 3x - 1 + 2 \] \[ y = 3x + 1 \]
The final equation after translating the line is: \[ y = 3x + 1 \]
Thus, the correct answer is B. y = 3x + 1.