To identify the correct graph of the function \( y = x + 2 \), we can analyze the characteristics of this linear equation.
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Slope and Intercept: The function \( y = x + 2 \) has a slope of 1 and a y-intercept of 2. This means:
- The line will rise at a 45-degree angle (upward slanting).
- The line will cross the y-axis at the point (0, 2).
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Key Points:
- When \( x = 0 \), \( y = 2 \) (so it passes through (0, 2)).
- When \( x = -2 \), \( y = 0 \) (so it passes through (-2, 0)).
- When \( x = 2 \), \( y = 4 \) (so it does not pass through (2, 0)).
Now, let's evaluate the options:
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Option A: A downward slanting line passing through (0, 2) and (2, 0). This does not represent \( y = x + 2 \) because it has a negative slope (downward).
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Option B: An upward slanting line passing through (-2, 0) and (0, 2). This represents \( y = x + 2 \) because it has a positive slope and the correct points.
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Option C: A parabola opening upward, which does not represent a linear function like \( y = x + 2 \).
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Option D: A circle, which also does not represent the linear function \( y = x + 2 \).
From this analysis, the correct graph for the function \( y = x + 2 \) is:
B. An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 4 to 4 in one unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through points plotted at (-2, 0) and (0, 2).
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