Question

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:

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