QQuestionMathematics
QuestionMathematics
Why does a horizontal line have a slope of 0, but a vertical line has an undefined slope?
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Answer
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Step 1:I'll solve this problem step by step, explaining the concept of slope for horizontal and vertical lines:
Step 2:: Understanding Slope
slope = \frac{rise}{run} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}
Slope is defined as the change in vertical distance (rise) divided by the change in horizontal distance (run):
Step 3:: Horizontal Line Analysis
- When we calculate slope: $$slope = \frac{0}{x_{2} - x_{1}} = 0
For a horizontal line: - The y-coordinate remains constant for all points - Regardless of the horizontal distance, the rise is always zero
Step 4:: Vertical Line Analysis
- When we try to calculate slope: $$slope = \frac{y_{2} - y_{1}}{0}
For a vertical line: - The x-coordinate remains constant for all points - Division by zero is mathematically undefined
Step 5:: Key Difference
- Horizontal line: Zero change in vertical direction - Vertical line: Zero change in horizontal direction, leading to division by zero
Final Answer
A horizontal line has a slope of 0 because there is no vertical change, while a vertical line has an undefined slope because it would require dividing by zero, which is mathematically impossible.
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