Question

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)Responsesy=−x+4y equals negative x plus 4y=x+3y equals x plus 3y=x+4y equals x plus 4y=3

Answer 1

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

1. **Translate 1 unit to the right**:
- When you translate a line to the right, you adjust the x-coordinate by subtracting 1.
- Substituting \( x - 1 \) into the equation gives:
\[
y = - (x - 1) + 1 = -x + 1 + 1 = -x + 2
\]

2. **Translate 2 units up**:
- When you translate a line up, you add 2 to the y-coordinate.
- Therefore, the equation becomes:
\[
y = -x + 2 + 2 = -x + 4
\]

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

Thus, the correct response is \( y = -x + 4 \).