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The question asks how the graph of the function \( y = x + 2 \) would compare to the graph of \( y = x - 1 \).

1. **Starting with the first function:**  
   \( y = x + 2 \) has a slope of 1 and a y-intercept at \( (0, 2) \). The graph is a straight line that crosses the y-axis at 2.

2. **For the second function:**  
   \( y = x - 1 \) has the same slope (1), meaning the lines will have the same steepness. The only difference is the y-intercept, which is now at \( (0, -1) \).

**Comparison:**
- The only difference between these two lines is the vertical shift. The first line is shifted 2 units up, and the second is shifted 1 unit down from that. Hence, the line for \( y = x - 1 \) will be **shifted down** compared to \( y = x + 2 \).

The correct answer is **A. It would be shifted down.**

Would you like further details on this? Here are five related questions to deepen your understanding:

1. How does changing the slope affect the graph of a linear function?
2. What happens to the graph if both the slope and y-intercept are changed?
3. How do horizontal shifts affect the graph of a function?
4. What is the significance of the slope in the equation \( y = mx + b \)?
5. Can the slope or y-intercept ever make the line steeper without shifting it vertically?

**Tip:** Always remember that changes to the constant term \( b \) in \( y = mx + b \) result in vertical shifts, while changes to the slope \( m \) affect the steepness.

If y = x + 2 were changed to y = x - 1, how would the graph of the new function compare with the first one?

Understand how the graph of y = x + 2 changes when it's transformed into y = x - 1. This problem covers the core concepts of linear functions and graph transformations, focusing on shifts in the y-intercept. Ideal for students in Grades 8-10.

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