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 x plus 4

y=−x+4
y equals negative x plus 4

y=3
y equals 3

y=x+3

Answer 1

To find the equation of the line after it has been translated, we start with the original line \( y = -x + 1 \).

1. **Translate 1 unit to the right**: To translate a line to the right, we replace \( x \) with \( x - 1 \). So, the equation becomes:
\[
y = -(x - 1) + 1 = -x + 1 + 1 = -x + 2
\]

2. **Translate 2 units up**: To translate a line up, we add the amount of the vertical translation to the entire equation. So we add 2 to the equation from step 1:
\[
y = (-x + 2) + 2 = -x + 4
\]

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

Thus, the correct response is:
**y = -x + 4 (y equals negative x plus 4)**.