Math Problem Statement
solve
Solution
To determine whether the given lines are parallel, perpendicular, or neither, we need to analyze their slopes. The equations of the lines given are:
These equations are in the slope-intercept form, , where is the slope and is the y-intercept.
- For the first equation , the slope .
- For the second equation , the slope .
Analysis:
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Parallel Lines: Two lines are parallel if their slopes are equal. Here, and , so the slopes are not equal. Therefore, the lines are not parallel.
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Perpendicular Lines: Two lines are perpendicular if the product of their slopes is . Let's check: Since , the lines are not perpendicular.
Conclusion:
The given lines are neither parallel nor perpendicular.
Would you like more details or have any other questions?
Here are some related questions you might consider:
- What are the characteristics of parallel lines?
- How do you find the slope from an equation not in slope-intercept form?
- Can lines with the same y-intercept ever be perpendicular?
- How would the problem change if one of the slopes were negative?
- What does the y-intercept tell us about a line?
Tip: Always check both slope and y-intercept when comparing lines. Even if they have the same y-intercept, their slopes determine if they are parallel or perpendicular.
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Math Problem Analysis
Mathematical Concepts
Slope
Parallel Lines
Perpendicular Lines
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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