Question
Question
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2
and −x+y=7
? Should the lines for the system be parallel?
(1 point)
Responses
The graph of −x+y=7
is incorrect. The lines should intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7
is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.
The graph of x+y=2
is incorrect. The lines should intersect.
Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The solid line passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2
and −x+y=7
? Should the lines for the system be parallel?
(1 point)
Responses
The graph of −x+y=7
is incorrect. The lines should intersect.
The graph of negative x plus y equals 7 is incorrect. The lines should intersect.
Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7
is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.
The graph of x+y=2
is incorrect. The lines should intersect.
Answers
Answered by
GPT-4o mini
To determine whether the graph is correct and if the lines should be parallel or intersect, we first need to analyze the given equations:
1. **First equation**: \(x + y = 2\)
- Rearranging gives \(y = -x + 2\).
- This line has a slope of -1 and a y-intercept at (0, 2).
2. **Second equation**: \(-x + y = 7\)
- Rearranging gives \(y = x + 7\).
- This line has a slope of 1 and a y-intercept at (0, 7).
Since the slopes of the two lines are different (-1 and 1), they will intersect at some point rather than being parallel.
From the description of the graph:
- The solid line passes through (0, 2) and (2, 0), which corresponds to the equation \(x + y = 2\) accurately.
- The dashed line, however, is described as passing through (-7, 0) and (7, 0). This corresponds to the equation \(y = 0\), which does not match the equation \(-x + y = 7\).
Thus, the correct answer to the question is:
**The graph of \(−x+y=7\) is incorrect. The lines should intersect.**
1. **First equation**: \(x + y = 2\)
- Rearranging gives \(y = -x + 2\).
- This line has a slope of -1 and a y-intercept at (0, 2).
2. **Second equation**: \(-x + y = 7\)
- Rearranging gives \(y = x + 7\).
- This line has a slope of 1 and a y-intercept at (0, 7).
Since the slopes of the two lines are different (-1 and 1), they will intersect at some point rather than being parallel.
From the description of the graph:
- The solid line passes through (0, 2) and (2, 0), which corresponds to the equation \(x + y = 2\) accurately.
- The dashed line, however, is described as passing through (-7, 0) and (7, 0). This corresponds to the equation \(y = 0\), which does not match the equation \(-x + y = 7\).
Thus, the correct answer to the question is:
**The graph of \(−x+y=7\) is incorrect. The lines should intersect.**