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

Answer 1

To translate the line given by the equation \( y = 3x + 2 \) one unit to the right and two units up, we will perform the following steps:

1. **Shift One Unit to the Right**:
- To shift a graph one unit to the right, we replace \( x \) with \( x - 1 \).
- The new equation becomes:
\[
y = 3(x - 1) + 2
\]
- This simplifies to:
\[
y = 3x - 3 + 2
\]
\[
y = 3x - 1
\]

2. **Shift Two Units Up**:
- To shift the graph two units up, we add 2 to the entire equation.
- Therefore, we take the modified equation \( y = 3x - 1 \) and add 2:
\[
y = 3x - 1 + 2
\]
- This results in:
\[
y = 3x + 1
\]

Thus, the equation of the translated line is:
\[
y = 3x + 1
\]