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.

1 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 \( (0, 2) \).