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 equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
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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 equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
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Answers
Answer
abcd ?
Answer
so is it abc or d
Answered by
GPT-4o mini
The statement is true, because the lines are parallel.
Explanation: The equation of the solid line is \( y = -x + 3 \) and the equation of the dashed line is \( x + y = 8 \). To analyze whether these lines intersect, we first need to rewrite the second equation in slope-intercept form:
1. Start with \( x + y = 8 \).
2. Rearrange to solve for \( y \):
\[
y = -x + 8.
\]
Now, we can see that both lines \( y = -x + 3 \) and \( y = -x + 8 \) have the same slope of -1. Since they have different y-intercepts (3 and 8), they are parallel lines and will never intersect. Therefore, there is no solution to the system of equations, confirming that the statement is true.
Explanation: The equation of the solid line is \( y = -x + 3 \) and the equation of the dashed line is \( x + y = 8 \). To analyze whether these lines intersect, we first need to rewrite the second equation in slope-intercept form:
1. Start with \( x + y = 8 \).
2. Rearrange to solve for \( y \):
\[
y = -x + 8.
\]
Now, we can see that both lines \( y = -x + 3 \) and \( y = -x + 8 \) have the same slope of -1. Since they have different y-intercepts (3 and 8), they are parallel lines and will never intersect. Therefore, there is no solution to the system of equations, confirming that the statement is true.
Answered by
GPT-4o mini
It seems like you might be looking for some options or answers related to the question or statement about the lines. If you need further clarification or specific options based on a particular context, please provide more details. Here’s a summary from the earlier explanation regarding the two lines:
- The solid line: \( y = -x + 3 \)
- The dashed line: \( y = -x + 8 \)
Since these two lines are parallel (same slope), they will never intersect, and thus the statement about having no solution to the system is true.
If you're asking for a multiple-choice answer (like letters a, b, c, or d), please provide the corresponding choices, and I can help identify or clarify the correct option!
- The solid line: \( y = -x + 3 \)
- The dashed line: \( y = -x + 8 \)
Since these two lines are parallel (same slope), they will never intersect, and thus the statement about having no solution to the system is true.
If you're asking for a multiple-choice answer (like letters a, b, c, or d), please provide the corresponding choices, and I can help identify or clarify the correct option!
Answered by
GPT-4o mini
Given the options you originally provided, the correct answer is:
**The statement is true, because the lines are parallel.**
This corresponds to the option: **"The statement is true, because the lines are parallel."**
If you had labeled your options as a, b, c, and d, please specify which letter corresponds to that option, and I can confirm if it's correct! Based on your options:
- a: The statement is false, because the lines are parallel.
- b: The statement is false, because the lines have an intersection point.
- c: The statement is true, because the lines have an intersection point.
- d: The statement is true, because the lines are parallel.
Correct answer: **d**.
**The statement is true, because the lines are parallel.**
This corresponds to the option: **"The statement is true, because the lines are parallel."**
If you had labeled your options as a, b, c, and d, please specify which letter corresponds to that option, and I can confirm if it's correct! Based on your options:
- a: The statement is false, because the lines are parallel.
- b: The statement is false, because the lines have an intersection point.
- c: The statement is true, because the lines have an intersection point.
- d: The statement is true, because the lines are parallel.
Correct answer: **d**.
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