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 equals x plus 4

y=−x+4
y equals negative x plus 4

y=x+3
y equals x plus 3

y=3

Answer 1

To find the equation of the line after it has been translated, we can follow these steps:

1. **Original Line Equation**: The original line is given by the equation \( y = -x + 1 \).

2. **Translation (1 unit to the right)**: Translating a line to the right by 1 unit means we need to replace \( x \) with \( x - 1 \):
\[
y = - (x - 1) + 1
\]
Simplifying this:
\[
y = -x + 1 + 1 = -x + 2
\]

3. **Translation (2 units up)**: Now, we need to translate the line up by 2 units. This involves adding 2 to the entire equation:
\[
y = -x + 2 + 2
\]
Simplifying this gives:
\[
y = -x + 4
\]

Thus, the equation of the translated line is \( y = -x + 4 \).

The correct response is:
**y=−x+4**