Which of the following is the graph of the function y=x+2
?(1 point)
Responses
A. 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.
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 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.
C. 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.
D. 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.
?(1 point)
Responses
A. 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.
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 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.
C. 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.
D. 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.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To identify the correct graph of the function \( y = x + 2 \), we can analyze the characteristics of this linear equation.
1. **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).
2. **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:
- **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).
- **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.
- **Option C**: A parabola opening upward, which does not represent a linear function like \( y = x + 2 \).
- **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).**
1. **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).
2. **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:
- **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).
- **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.
- **Option C**: A parabola opening upward, which does not represent a linear function like \( y = x + 2 \).
- **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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