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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?

Hint: try graphing
A. y=-x+4
B. y=x+3
C. y=x+4
D. y=3

1 answer

To find the equation of the line after it has been translated, we can follow these steps:

  1. Identify the original line: The original line is given by the equation \( y = -x + 1 \).

  2. Translate the line:

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

    • Translate 2 units up: To translate the line 2 units up, we add 2 to the entire equation: \[ y = -x + 2 + 2 = -x + 4 \]

  3. Final equation: After both translations, the new equation is \( y = -x + 4 \).

Therefore, the equation of the translated line is \(\boxed{A}\) \(y = -x + 4\).