The line y = —x + 1 is drawn on the coordinate plane. It is translated 1 unit to the right and 2 units up. What is the equation of the translated line? (1 point)

Question

0y=3
Oy=-x+4
0 y=x+1
0 y=x +3

Answer 1

To translate the line \( y = -x + 1 \) 1 unit to the right and 2 units up, we follow these steps:

1. Translation 1 unit to the right: To move a line to the right, we replace \( x \) with \( x - 1 \). Therefore, the new equation after the horizontal translation is: \[ y = -(x - 1) + 1 = -x + 1 + 1 = -x + 2 \]

2. Translation 2 units up: To move a line up, we add the number of units to the \( y \)-value. So, we modify the equation obtained in the first step: \[ y = -x + 2 + 2 = -x + 4 \]

Thus, the equation of the translated line is: \[ y = -x + 4 \]

The correct answer is: \( y = -x + 4 \).