To find the equation of the line after it has been translated, we start with the original line \( y = -x + 1 \).
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Translate 1 unit to the right: To translate a line to the right, we replace \( x \) with \( x - 1 \). So, the equation becomes: \[ y = -(x - 1) + 1 = -x + 1 + 1 = -x + 2 \]
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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).