To determine which graph represents the equation $y = x + 2$, let's analyze the key features of this line:

1. Slope: The equation $y = x + 2$ has a slope of 1, meaning it rises one unit vertically for each unit it moves horizontally. This creates a line that goes diagonally upward to the right at a 45-degree angle.

2. Y-intercept: The y-intercept is 2, indicating that the line crosses the y-axis at the point (0, 2).

Now let's examine each option:

• Option A: This line passes through the y-axis at $y = 2$ and has a positive slope of 1. It matches the equation $y = x + 2$.
• Option B: This line passes through a different y-intercept, so it does not match.
• Option C: This line passes through a different y-intercept as well.
• Option D: This line has a different slope or intercept.

Answer: The correct option is A.

Would you like more details or have questions on this topic?

Additional Related Questions:

1. How do we determine the slope of a line from an equation?
2. How would the graph change if the equation were $y = x - 2$?
3. What does a positive slope indicate about the direction of a line?
4. How can we recognize parallel lines by comparing their equations?
5. What are the steps to find the x-intercept of a line?

Tip: Remember, the y-intercept is the value of $y$ when $x = 0$.