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=3 y equals 3 y=x+3 y equals x plus 3 y=x+4 y equals x plus 4 y=−x+4

Select One

Answer 1

To find the equation of the translated line, we first start with the original equation of the line, which is \( y = -x + 1 \).

When we translate the line:

1. **Translation 1 unit to the right:**
- To translate right by 1 unit, we replace \( x \) with \( x - 1 \).
- The equation becomes:
\[
y = - (x - 1) + 1 = -x + 1 + 1 = -x + 2
\]

2. **Translation 2 units up:**
- To translate up by 2 units, we add 2 to the entire equation.
- The equation becomes:
\[
y = -x + 2 + 2 = -x + 4
\]

Thus, the final equation of the translated line is:
\[
y = -x + 4
\]

So, the correct response is:
**y = −x + 4**.