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Graph the linear equation y=−3x+2.(1 point) Responses A coordinate plane shows the x-axis ranging from negative 9 to 9 in incre...Asked by Lee Hooni 🖤
Graph the linear equation
y=2/3x−1.
(1 point)
Responses
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.
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y=2/3x−1.
(1 point)
Responses
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 2 right parenthesis, and left parenthesis 1 comma negative 9 right parenthesis.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 4 right parenthesis and left parenthesis 1 comma 2 right parenthesis.
A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 3 comma 1 right parenthesis.
An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.
Image with alt text: An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis negative 2 comma negative 2 right parenthesis and left parenthesis 0 comma 1 right parenthesis.
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To graph the linear equation \( y = \frac{2}{3}x - 1 \), we can follow these steps:
1. **Identify the slope and y-intercept**:
- The equation is in slope-intercept form \( y = mx + b \), where:
- \( m = \frac{2}{3} \) (the slope)
- \( b = -1 \) (the y-intercept)
2. **Plot the y-intercept**:
- Start by plotting the point where the line crosses the y-axis. This occurs at \( (0, -1) \).
3. **Use the slope**:
- From the y-intercept \( (0, -1) \), the slope \( \frac{2}{3} \) means you can go up 2 units and to the right 3 units. This will give you another point:
- Starting from \( (0, -1) \), move up 2 to \( (0, 1) \) and right 3 to \( (3, 1) \). So, plot the point \( (3, 1) \).
4. **Draw the line**:
- Draw a straight line through the points \( (0, -1) \) and \( (3, 1) \), and extend it with arrows on both ends.
5. **Check for other points**:
- You can verify by substituting additional values for \( x \) (negative or beyond the plotted points) to ensure the line is accurate.
In the response options, you should look for a plot that accurately reflects the points \( (0, -1) \) and \( (3, 1) \), following the slope of \( \frac{2}{3} \).
If the graphed points and line correctly show this behavior, that is your answer. The correct description is likely:
- A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: \( (0, -1) \) and \( (3, 1) \).
This description accurately reflects the graph for the equation \( y = \frac{2}{3}x - 1 \).
1. **Identify the slope and y-intercept**:
- The equation is in slope-intercept form \( y = mx + b \), where:
- \( m = \frac{2}{3} \) (the slope)
- \( b = -1 \) (the y-intercept)
2. **Plot the y-intercept**:
- Start by plotting the point where the line crosses the y-axis. This occurs at \( (0, -1) \).
3. **Use the slope**:
- From the y-intercept \( (0, -1) \), the slope \( \frac{2}{3} \) means you can go up 2 units and to the right 3 units. This will give you another point:
- Starting from \( (0, -1) \), move up 2 to \( (0, 1) \) and right 3 to \( (3, 1) \). So, plot the point \( (3, 1) \).
4. **Draw the line**:
- Draw a straight line through the points \( (0, -1) \) and \( (3, 1) \), and extend it with arrows on both ends.
5. **Check for other points**:
- You can verify by substituting additional values for \( x \) (negative or beyond the plotted points) to ensure the line is accurate.
In the response options, you should look for a plot that accurately reflects the points \( (0, -1) \) and \( (3, 1) \), following the slope of \( \frac{2}{3} \).
If the graphed points and line correctly show this behavior, that is your answer. The correct description is likely:
- A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: \( (0, -1) \) and \( (3, 1) \).
This description accurately reflects the graph for the equation \( y = \frac{2}{3}x - 1 \).
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