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)
Responses

y=−x+4
y equals negative x plus 4

y=3
y equals 3

y=x+4
y equals x plus 4

y=x+3
y equals x plus 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**: To move the line to the right, we replace \( x \) with \( x - 1 \) in the equation.
\[
y = -(x - 1) + 1 = -x + 1 + 1 = -x + 2
\]

2. **Translate 2 units up**: To move the line up, we add 2 to the entire equation.
\[
y = -x + 2 + 2 = -x + 4
\]

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

Thus, the correct response is:
**y = -x + 4**.