Slope of Vertical Line

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

  1. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Why does the slope of a vertical line not exist? Can you provide a geometric interpretation?
     
    nycmathguy, Jul 31, 2022
    #1
  2. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    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
    #2
    nycmathguy likes this.
  3. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    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
    #3
  4. nycmathguy

    MathLover1

    Joined:
    Jun 27, 2021
    Messages:
    2,989
    Likes Received:
    2,884
    yes
     
    MathLover1, Aug 1, 2022
    #4
    nycmathguy likes this.
  5. nycmathguy

    nycmathguy

    Joined:
    Jun 27, 2021
    Messages:
    5,386
    Likes Received:
    422
    Interesting.
     
    nycmathguy, Aug 1, 2022
    #5
  6. nycmathguy

    HallsofIvy

    Joined:
    Nov 6, 2021
    Messages:
    161
    Likes Received:
    78
    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
    #6
  7. nycmathguy

    e.jane.aran

    Joined:
    Aug 13, 2023
    Messages:
    32
    Likes Received:
    28
    (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
    #7
    sologuitar likes this.
  8. nycmathguy

    sologuitar

    Joined:
    Aug 11, 2023
    Messages:
    21
    Likes Received:
    2
    Hi. Thank you.
     
    sologuitar, Sep 12, 2023
    #8
  9. nycmathguy

    conway

    Joined:
    Nov 28, 2023
    Messages:
    83
    Likes Received:
    4
    A vertical slope has a "steepness" that is VERTICAL. Ask a mountain climber if a vertical slope exists. They will say yes. They problem is division by zero. The problem is mathematics. Consider a horizontal slope. It exists and is definable in mathematics. Yet what is its "steepness"?

    Some will say a number cannot be "vertical". How then can a number "horizontal". As again horizontal slopes are definable.
     
    conway, Mar 14, 2024
    #9
  10. nycmathguy

    HallsofIvy

    Joined:
    Nov 6, 2021
    Messages:
    161
    Likes Received:
    78
    NUMBERS are neither horizontal nor vertical. Those are geometric concepts. While lines are geometric and can have slope, can be horizontal or vertical, numbers are not. Yes, lines have a "steepness" and can be vertical that is not what we are discussing here. The "slope" of a line is a number measuing the steepness. It is the tangent of the angle the line makes with the horizontal (or cotangent of the angle with vertical. Neither tangent of 90 degrees nor cotangent of 0 degrees is defined- there is no number associated with them. A horizontal line has slope tan(0)= cot(90)= 0 but a vertical line has NO slope because tan(90) and cot(0) are not defined.
     
    HallsofIvy, Mar 17, 2024
    #10
    conway likes this.
  11. nycmathguy

    conway

    Joined:
    Nov 28, 2023
    Messages:
    83
    Likes Received:
    4
    So if they were defined...

    0 = horizontal

    a/a = "a slope" if a=/=0

    a = "vertical" for any a=/= 0

    again the only thing holding mathematics back from defining a vertical slope is division by zero.
     
    conway, Mar 18, 2024
    #11
Ask a Question

Want to reply to this thread or ask your own question?

You'll need to choose a username for the site, which only take a couple of moments (here). After that, you can post your question and our members will help you out.
Similar Threads
Loading...