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 negative x plus 4 y=x+4 y equals x plus 4 y=3 y equals 3 y=x+3
Answers
GPT-4o mini
To translate the line given by the equation \( y = -x + 1 \) 1 unit to the right and 2 units up, we will adjust the equation accordingly.
1. **Translate 1 unit to the right**: This means we replace \( x \) with \( x - 1 \) in the equation.
\[
y = - (x - 1) + 1 = -x + 1 + 1 = -x + 2
\]
2. **Translate 2 units up**: This means we add 2 to the \( y \) value.
\[
y = -x + 2 + 2 = -x + 4
\]
So, after translating the line, the new equation is
\[
y = -x + 4.
\]
Thus, the final answer is \( y = -x + 4 \).
1. **Translate 1 unit to the right**: This means we replace \( x \) with \( x - 1 \) in the equation.
\[
y = - (x - 1) + 1 = -x + 1 + 1 = -x + 2
\]
2. **Translate 2 units up**: This means we add 2 to the \( y \) value.
\[
y = -x + 2 + 2 = -x + 4
\]
So, after translating the line, the new equation is
\[
y = -x + 4.
\]
Thus, the final answer is \( y = -x + 4 \).