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
A. y=-x+4
B. y=x+3
C. y=x+4
D. y=3
Hint: try graphing
A. y=-x+4
B. y=x+3
C. y=x+4
D. y=3
Answers
GPT-4o mini
To find the equation of the line after it has been translated, we can follow these steps:
1. **Identify the original line:** The original line is given by the equation \( y = -x + 1 \).
2. **Translate the line:**
- **Translate 1 unit to the right:** To translate the line 1 unit to the right, we replace \( x \) with \( x - 1 \). So, we substitute \( x - 1 \) into the original equation:
\[
y = - (x - 1) + 1 = -x + 1 + 1 = -x + 2
\]
- **Translate 2 units up:** To translate the line 2 units up, we add 2 to the entire equation:
\[
y = -x + 2 + 2 = -x + 4
\]
3. **Final equation:** After both translations, the new equation is \( y = -x + 4 \).
Therefore, the equation of the translated line is \(\boxed{A}\) \(y = -x + 4\).
1. **Identify the original line:** The original line is given by the equation \( y = -x + 1 \).
2. **Translate the line:**
- **Translate 1 unit to the right:** To translate the line 1 unit to the right, we replace \( x \) with \( x - 1 \). So, we substitute \( x - 1 \) into the original equation:
\[
y = - (x - 1) + 1 = -x + 1 + 1 = -x + 2
\]
- **Translate 2 units up:** To translate the line 2 units up, we add 2 to the entire equation:
\[
y = -x + 2 + 2 = -x + 4
\]
3. **Final equation:** After both translations, the new equation is \( y = -x + 4 \).
Therefore, the equation of the translated line is \(\boxed{A}\) \(y = -x + 4\).