1. **State the problem:** We have an original line given by the equation $y = x + 1$ and its transformed image line $y = x + 2$. We need to find the transforming vector that moves the original line to the image line. 2. **Understand the transformation:** The lines have the same slope ($1$), so the transformation is a vertical translation. 3. **Formula for translation vector:** A translation vector is given by $\vec{v} = (\Delta x, \Delta y)$ where $\Delta x$ and $\Delta y$ are the horizontal and vertical shifts respectively. 4. **Calculate the vertical shift:** The original line has $y$-intercept $1$, and the image line has $y$-intercept $2$. So, $\Delta y = 2 - 1 = 1$. 5. **Calculate the horizontal shift:** Since the slope is unchanged and the lines are parallel, $\Delta x = 0$. 6. **Conclusion:** The transforming vector is $$\vec{v} = (0, 1)$$ which means the line is shifted up by 1 unit.