Lucy draws a line with the equation y=3x+2

Question

. She translates the line by shifting it one unit to the right and two units up. Which is the equation of the new line?(1 point)
Responses

y=3x−1
y equals 3 x minus 1

y=3x+1
y equals 3 x plus 1

y=4x+2
y equals 4 x plus 2

y=5x+3

Answer 1

To translate the line given by the equation \( y = 3x + 2 \) one unit to the right and two units up, we can follow these steps:

1. Translating one unit to the right: To shift a function to the right, we replace \( x \) with \( x - 1 \). This gives us the new equation: \[ y = 3(x - 1) + 2 \] Simplifying this: \[ y = 3x - 3 + 2 = 3x - 1 \]

2. Translating two units up: To shift the function up, we add 2 to the entire equation: \[ y = (3x - 1) + 2 = 3x + 1 \]

Thus, the equation of the new line after the translation is: \[ y = 3x + 1 \]

So the correct response is: y = 3x + 1.