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? Hint: Try graphing (1 point) Responses y = -x + 4 y = -x + 4 y = x + 3 y = x + 3 y = x + 4 y = x + 4 y = 3

Answer 1

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

1. Translation 1 unit to the right: This affects the \( x \)-coordinate, so we replace \( x \) with \( x - 1 \) in the equation:

   \[ y = - (x - 1) + 1 \]

   Simplifying this, we get:

   \[ y = -x + 1 + 1 = -x + 2 \]

2. Translation 2 units up: This affects the \( y \)-coordinate, so we add 2 to the \( y \) value:

   \[ y = -x + 2 + 2 = -x + 4 \]

The final equation of the translated line is:

\[ y = -x + 4 \]

Thus, the answer is:

y = -x + 4.