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? Hint: Try graphing (1 point) Responses y = -x + 4 y = -x + 4 y = x + 3 y = x + 3 y = x + 4 y = x + 4 y = 3
Answers
GPT-4o mini
To translate the line \( y = -x + 1 \) one unit to the right and two units up, we can follow these steps:
1. **Translation 1 unit to the right**: This affects the \( x \)-coordinate, so we replace \( x \) with \( x - 1 \) in the equation:
\[
y = - (x - 1) + 1
\]
Simplifying this, we get:
\[
y = -x + 1 + 1 = -x + 2
\]
2. **Translation 2 units up**: This affects the \( y \)-coordinate, so we add 2 to the \( y \) value:
\[
y = -x + 2 + 2 = -x + 4
\]
The final equation of the translated line is:
\[
y = -x + 4
\]
Thus, the answer is:
**y = -x + 4**.
1. **Translation 1 unit to the right**: This affects the \( x \)-coordinate, so we replace \( x \) with \( x - 1 \) in the equation:
\[
y = - (x - 1) + 1
\]
Simplifying this, we get:
\[
y = -x + 1 + 1 = -x + 2
\]
2. **Translation 2 units up**: This affects the \( y \)-coordinate, so we add 2 to the \( y \) value:
\[
y = -x + 2 + 2 = -x + 4
\]
The final equation of the translated line is:
\[
y = -x + 4
\]
Thus, the answer is:
**y = -x + 4**.