Question
Lucy draws a line with the equation y=3x+2 . She translates the line by shifting it one unit to the right and two units up. Which is the equation of the new line?(1 point) Responses y=5x+3 y equals 5 x plus 3 y=3x+1 y equals 3 x plus 1 y=4x+2 y equals 4 x plus 2 y=3x−1
Answers
GPT-4o mini
To translate the line represented by the equation \( y = 3x + 2 \), we need to shift it one unit to the right and two units up.
1. **Shift the line one unit to the right**:
- To shift the graph one unit to the right, we replace \( x \) with \( x - 1 \) in the equation.
- The equation becomes:
\[
y = 3(x - 1) + 2 = 3x - 3 + 2 = 3x - 1
\]
2. **Shift the line two units up**:
- To shift the graph two units up, we add 2 to the entire equation.
- So we take our current equation \( y = 3x - 1 \) and add 2:
\[
y = 3x - 1 + 2 = 3x + 1
\]
Thus, after translating the line, the equation of the new line is:
\[
y = 3x + 1
\]
Therefore, the correct response is:
y = 3x + 1
1. **Shift the line one unit to the right**:
- To shift the graph one unit to the right, we replace \( x \) with \( x - 1 \) in the equation.
- The equation becomes:
\[
y = 3(x - 1) + 2 = 3x - 3 + 2 = 3x - 1
\]
2. **Shift the line two units up**:
- To shift the graph two units up, we add 2 to the entire equation.
- So we take our current equation \( y = 3x - 1 \) and add 2:
\[
y = 3x - 1 + 2 = 3x + 1
\]
Thus, after translating the line, the equation of the new line is:
\[
y = 3x + 1
\]
Therefore, the correct response is:
y = 3x + 1