To find the equation of the new line after translating the line given by the equation \(y = 3x + 2\) one unit to the right and two units up, we need to understand how translations affect the equation of the line.
- Shifting a line one unit to the right means replacing \(x\) with \(x - 1\) in the equation.
- Shifting the line two units up means adding 2 to the entire equation.
Starting with the original equation: \[ y = 3x + 2 \]
Step 1: Shift one unit to the right: Replace \(x\) with \(x - 1\): \[ y = 3(x - 1) + 2 \] \[ y = 3x - 3 + 2 \] \[ y = 3x - 1 \]
Step 2: Shift two units up: Now add 2 to the entire equation: \[ y = 3x - 1 + 2 \] \[ y = 3x + 1 \]
Thus, the equation of the new line is: \[ y = 3x + 1 \]
So the correct answer is \(A. y = 3x + 1\).