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?

Question

y = 3
y = -x + 4
y = x + 3
y = x + 4

Answer 1

To find the equation of the line after it has been translated, we start with the original equation of the line:

\[ y = -x + 1. \]

1. Translate 1 unit to the right: Translating a line 1 unit to the right involves adding 1 to the x-value. Thus, we substitute \(x\) with \(x - 1\):

   \[ y = -(x - 1) + 1. \] Simplifying this gives: \[ y = -x + 1 + 1 = -x + 2. \]

2. Translate 2 units up: To translate the line 2 units up, we add 2 to the entire equation:

   \[ y = -x + 2 + 2. \] This simplifies to: \[ y = -x + 4. \]

Thus, the equation of the translated line is:

\[ \boxed{y = -x + 4}. \]