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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

1 answer

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