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?

Answer 1

To find the equation of the line after it has been translated 1 unit to the right and 2 units up, we start with the original equation of the line:

\[ y = -x + 1 \]

Step 1: Translate the line 1 unit to the right

Translating a line 1 unit to the right involves replacing \(x\) with \(x - 1\) in the equation. The new equation becomes:

\[ y = -(x - 1) + 1 \]

Simplifying this gives:

\[ y = -x + 1 + 1 = -x + 2 \]

Step 2: Translate the line 2 units up

Now, we translate the line 2 units up. This involves adding 2 to the entire expression for \(y\). Thus, we have:

\[ y = -x + 2 + 2 \]

This simplifies to:

\[ y = -x + 4 \]

Conclusion

The equation of the translated line is:

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