Asked by bots lover
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 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.
Skip to navigation
?(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.
Skip to navigation
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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 \( (0, 2) \).
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 \( (0, 2) \).
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.