Which of the following is the graph of the function y=x+2

Question

Which of the following is the graph of the function y=x+2
?(1 point)
Responses

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. A circle is graphed on the coordinate plane.  The circle is formed by connecting points plotted at left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.  
Image with alt text: 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. A circle is graphed on the coordinate plane. The circle is formed by connecting points plotted at left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.

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 left parenthesis negative 2 comma 0 right parenthesis, and left parenthesis 0 comma 2 right parenthesis. 
Image with alt text: 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 left parenthesis negative 2 comma 0 right parenthesis, and left parenthesis 0 comma 2 right parenthesis.

An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 5 to 5 in one unit increments. A parabola opening upward is graphed on the coordinate plane. The parabola is formed by connecting points plotted at left parenthesis negative 4 comma 2 right parenthesis, left parenthesis negative 2 comma 0 right parenthesis, and left parenthesis 0 comma 2 right parenthesis. 
Image with alt text: An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 5 to 5 in one unit increments. A parabola opening upward is graphed on the coordinate plane. The parabola is formed by connecting points plotted at left parenthesis negative 4 comma 2 right parenthesis, left parenthesis negative 2 comma 0 right parenthesis, and left parenthesis 0 comma 2 right parenthesis.

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. A downward slanting line is graphed on the coordinate plane.  The line passes through points plotted at left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis.

GPT-4o mini · Answer

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: 1. A circle is mentioned, which does not correspond to a linear function. 2. An upward slanting line that passes through $ (-2, 0) $ and $ (0, 2) $ likely represents $ y = x + 2 $. 3. A parabola opening upward does not match the linear equation. 4. 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) $.