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?

A. y = 3
B. y = x + 4
C. y = -x + 4
D. y=x+3

Answer 1

To determine the equation of the translated line, we start with the original line given by \( y = -x + 1 \).

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

2. **Translation 2 units up**:
Now we need to translate the line \( y = -x + 2 \) 2 units up. To do this, we add 2 to the entire equation:
\[
y = -x + 2 + 2 = -x + 4
\]

Thus, the equation of the translated line is:

\[
y = -x + 4
\]

Looking at the provided options, the correct answer is:

**C. \( y = -x + 4 \)**.