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?



(1 point)
Responses

y = -x + 4

y = x + 3

y = x + 4

y = 3

Answer 1

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

\( y = -x + 1 \).

### Step 1: Translation of 1 unit to the right
When we translate the graph of a function \( y = f(x) \) to the right by \( h \) units, we replace \( x \) with \( x - h \). For \( h = 1 \), we replace \( x \) with \( x - 1 \):

\[
y = - (x - 1) + 1 = -x + 1 + 1 = -x + 2.
\]

### Step 2: Translation of 2 units up
Next, we translate the line \( y = -x + 2 \) upwards by 2 units. To do this, we add 2 to the output:

\[
y = -x + 2 + 2 = -x + 4.
\]

### Conclusion
After both translations, the equation of the line becomes:

\[
y = -x + 4.
\]

Therefore, the answer is:

**y = -x + 4**.