The function \( y = x + 2 \) represents a linear equation with a slope of 1 and a y-intercept of 2. To find the graph of this function, we can identify certain key points:
- When \( x = 0 \), \( y = 0 + 2 = 2 \). This gives us the point \( (0, 2) \).
- When \( x = -2 \), \( y = -2 + 2 = 0 \). This gives us the point \( (-2, 0) \).
- When \( x = 2 \), \( y = 2 + 2 = 4 \). This gives us the point \( (2, 4) \).
With these points, we see that the line rises from left to right and crosses through \( (0, 2) \) and \( (-2, 0) \).
From the options provided:
- A circle is mentioned, which does not correspond to a linear function.
- An upward slanting line that passes through \( (-2, 0) \) and \( (0, 2) \) likely represents \( y = x + 2 \).
- A parabola opening upward does not match the linear equation.
- A downward slanting line does not correspond to a positive slope.
Therefore, the correct graph of the function \( y = x + 2 \) is the illustration showing the upward slanting line passing through points \( (-2, 0) \) and \( (0, 2) \).