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):

Final Answer

- A horizontal line has a slope of 0 because there is no vertical change (rise = 0) - A vertical line has an undefined slope because division by zero is mathematically impossible (run = 0)