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+3y equals x plus 3y=x+4y equals x plus 4y=3y equals 3y=−x+4

Answer 1

To find the equation of the translated line, we need to apply the translations to the original line \( y = -x + 1 \).

1. **Translation 1 unit to the right**:
- This means we replace \( x \) with \( x - 1 \) in the equation of the line.
- The equation becomes:
\[
y = - (x - 1) + 1 = -x + 1 + 1 = -x + 2
\]

2. **Translation 2 units up**:
- Now, we add 2 to the \( y \) in the new equation.
- The equation becomes:
\[
y = -x + 2 + 2 = -x + 4
\]

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

So the answer is:
**y = -x + 4**.