Slope of Vertical Line

Discussion in 'Off-Topic Chat' started by nycmathguy, Jul 31, 2022.

  1. nycmathguy

    nycmathguy

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    Why does the slope of a vertical line not exist? Can you provide a geometric interpretation?
     
    nycmathguy, Jul 31, 2022
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  2. nycmathguy

    MathLover1

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    Vertical lines have an undefined slope because the horizontal change is 0 — you cannot divide a number by 0.

    The slope of a line is a measure of its steepness. Vertical lines have NO SLOPE.

    [​IMG]
     
    MathLover1, Jul 31, 2022
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  3. nycmathguy

    nycmathguy

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    Vertical lines cross the x-axis where y = 0. Can this also be a reason why vertical lines have no slope? I understand the steepness explanation.
     
    nycmathguy, Aug 1, 2022
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  4. nycmathguy

    MathLover1

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    yes
     
    MathLover1, Aug 1, 2022
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  5. nycmathguy

    nycmathguy

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    Interesting.
     
    nycmathguy, Aug 1, 2022
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  6. nycmathguy

    HallsofIvy

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    Considering lines making angle $\theta$ with the positive x-axis. Its slope is $tan(\theta)$. The limit, as $\theta$ goes to $\frac{\pi}{2}%, $tan(\theta)$ goes to infinity.
     
    HallsofIvy, Sep 11, 2023
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  7. nycmathguy

    e.jane.aran

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    (Above image scraped from Purplemath. To see it in context, try [here].)

    No. The line \(y = x\) also crosses the \(x\)-axis at the origin (that is, where \(y = 0\)), but this line has a slope of \(m = 1\), not zero.

    P.S. Hi, Sologuitar! :)
     
    e.jane.aran, Sep 11, 2023
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  8. nycmathguy

    sologuitar

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    Hi. Thank you.
     
    sologuitar, Sep 12, 2023
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