Question
Which statement is true for the slopes of parallel lines?
which answer is correct and why
a. Parallel lines have slopes that are undefined
b. parallel lines have a slope of zero
c. Parallel lines have slopes that are negative reciprocals of each other.
d. parallel lines have the same slope
which answer is correct and why
a. Parallel lines have slopes that are undefined
b. parallel lines have a slope of zero
c. Parallel lines have slopes that are negative reciprocals of each other.
d. parallel lines have the same slope
Answers
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Answered by
GPT-4o mini
The correct answer is:
**d. Parallel lines have the same slope.**
### Explanation:
- **a. Parallel lines have slopes that are undefined**: This is not true for all parallel lines. It is only true for vertical lines, which are a specific case. However, not all parallel lines are vertical.
- **b. Parallel lines have a slope of zero**: This statement applies to horizontal lines specifically, but not all parallel lines are horizontal. Therefore, this is also not true for all parallel lines.
- **c. Parallel lines have slopes that are negative reciprocals of each other**: This is false. Negative reciprocals apply to perpendicular lines, not parallel lines. For example, if one line has a slope of 2, a line perpendicular to it would have a slope of -1/2, while a parallel line would have the same slope of 2.
- **d. Parallel lines have the same slope**: This statement is true. By definition, parallel lines never intersect and therefore have identical slopes.
Thus, option **d** accurately describes the relationship between the slopes of parallel lines.
**d. Parallel lines have the same slope.**
### Explanation:
- **a. Parallel lines have slopes that are undefined**: This is not true for all parallel lines. It is only true for vertical lines, which are a specific case. However, not all parallel lines are vertical.
- **b. Parallel lines have a slope of zero**: This statement applies to horizontal lines specifically, but not all parallel lines are horizontal. Therefore, this is also not true for all parallel lines.
- **c. Parallel lines have slopes that are negative reciprocals of each other**: This is false. Negative reciprocals apply to perpendicular lines, not parallel lines. For example, if one line has a slope of 2, a line perpendicular to it would have a slope of -1/2, while a parallel line would have the same slope of 2.
- **d. Parallel lines have the same slope**: This statement is true. By definition, parallel lines never intersect and therefore have identical slopes.
Thus, option **d** accurately describes the relationship between the slopes of parallel lines.
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