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

Question

?(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 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.
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 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.

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 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.
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Answer 1

The function \( y = x + 2 \) represents a linear equation with a positive slope. To find the graph of this function, we need to identify its characteristics:

1. Slope: The slope is \( 1 \), meaning for every unit increase in \( x \), \( y \) increases by \( 1 \).

2. Y-intercept: The y-intercept is \( 2 \) (the point where the line crosses the y-axis), which occurs at the point \( (0, 2) \).

3. X-intercept: The x-intercept occurs when \( y = 0 \). Setting \( 0 = x + 2 \) gives \( x = -2 \), so the x-intercept is at the point \( (-2, 0) \).

Given these calculations, \( y = x + 2 \) is a straight line passing through the points \( (0, 2) \) and \( (-2, 0) \), and it goes upward as \( x \) increases.

From your description of the responses:

• The first option describes a downward slanting line, which does not match \( y = x + 2 \).
• The second option describes a parabola, which is also incorrect.
• The third option describes a circle, which is not correct for a linear function.
• The fourth option describes an upward slanting line that passes through the correct points \( (-2, 0) \) and \( (0, 2) \).

Thus, the correct graph for the function \( y = x + 2 \) is the fourth option: the upward slanting line that passes through the points \( (-2, 0) \) and \( (0, 2) \).