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Which graph shows the solution of −3x−y=3 and y=−3x+4?(1 point) Responses Two intersecting lines are graphed across a coordinat...Question
Which graph shows the solution of −3x−y=3 and y=−3x+4?(1 point)
Responses
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
Image with alt text: Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
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Responses
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two intersecting lines are graphed across a coordinate plane.
Image with alt text: Two intersecting lines are graphed across a coordinate plane.
Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
Image with alt text: Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid.
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Answers
Answer
which option
Answer
no option 1 2 3 or 4
Answered by
GPT-4o mini
To determine the type of graph that represents the equations \(-3x - y = 3\) and \(y = -3x + 4\), we first need to analyze the equations.
1. **Equation 1: \(-3x - y = 3\)**
We can rearrange this equation into slope-intercept form (y = mx + b):
\[
-y = 3 + 3x \implies y = -3x - 3
\]
This line has a slope of -3 and a y-intercept of -3.
2. **Equation 2: \(y = -3x + 4\)**
This equation is already in slope-intercept form. It has a slope of -3 and a y-intercept of 4.
Now we can compare the slopes and y-intercepts of both lines:
- Both lines have the same slope of -3.
- The first line (\(y = -3x - 3\)) has a y-intercept of -3, whereas the second line (\(y = -3x + 4\)) has a y-intercept of 4.
Since the two lines have the same slope but different y-intercepts, they are parallel.
Thus, the graph that represents the solution of the equations will show **two parallel lines**.
### Conclusion:
The response that describes "Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid" correctly represents the solution to the equations provided.
1. **Equation 1: \(-3x - y = 3\)**
We can rearrange this equation into slope-intercept form (y = mx + b):
\[
-y = 3 + 3x \implies y = -3x - 3
\]
This line has a slope of -3 and a y-intercept of -3.
2. **Equation 2: \(y = -3x + 4\)**
This equation is already in slope-intercept form. It has a slope of -3 and a y-intercept of 4.
Now we can compare the slopes and y-intercepts of both lines:
- Both lines have the same slope of -3.
- The first line (\(y = -3x - 3\)) has a y-intercept of -3, whereas the second line (\(y = -3x + 4\)) has a y-intercept of 4.
Since the two lines have the same slope but different y-intercepts, they are parallel.
Thus, the graph that represents the solution of the equations will show **two parallel lines**.
### Conclusion:
The response that describes "Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid" correctly represents the solution to the equations provided.
Answered by
GPT-4o mini
The correct option based on the analysis is:
**"Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid."**
This indicates that the two equations represent parallel lines due to having the same slope but different y-intercepts.
**"Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid."**
This indicates that the two equations represent parallel lines due to having the same slope but different y-intercepts.
Answered by
GPT-4o mini
I apologize for the confusion. Based on your description, it sounds like the options you provided correspond to specific choices. Since I don't have visual access to the options labeled 1, 2, 3, or 4, I cannot directly select one for you.
However, based on the analysis, since the lines are parallel, you should choose the option that indicates:
**Option 4: "Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid."**
This would be the correct choice. If there is anything else you need help with, please let me know!
However, based on the analysis, since the lines are parallel, you should choose the option that indicates:
**Option 4: "Two parallel lines are graphed across a coordinate plane. One line is dotted while the other is solid."**
This would be the correct choice. If there is anything else you need help with, please let me know!