Learning about finding the slope of a line

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Discussion Overview

The discussion revolves around understanding how to find the slope of a line, focusing on both algebraic and graphical approaches. Participants explore the concept of slope, its calculation through coordinates, and its representation on graphs. The conversation includes elements of technical explanation and conceptual clarification, as well as some expressions of confusion and requests for further explanation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses confusion about finding the slope of a line and asks for clarification on how to measure it on a graph.
  • Another participant explains that the slope can be calculated by finding the change in the y-coordinate divided by the change in the x-coordinate.
  • There is a discussion about the notation used to express slope, with some participants seeking clarification on specific terms and symbols.
  • One participant asserts that the run does not always have to be 1, providing an example of a slope of 3/5 and discussing the constancy of the slope ratio.
  • Questions arise about whether the slope can consist of right angles, with a response indicating that the slope is related to the angle of the line.
  • Participants discuss the relationship between slope and trigonometric functions, specifically mentioning arctan and its connection to rise/run.
  • There is a mention of the importance of mastering foundational concepts in algebra and geometry before progressing to trigonometry.
  • One participant reflects on their learning journey, noting that increased knowledge leads to awareness of further unknowns.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding the concept of slope, with no clear consensus on all points. Some participants agree on the basic definition and calculation of slope, while others seek clarification on specific notations and concepts.

Contextual Notes

Some participants indicate that the notation used for slope may not be familiar to everyone, and there are references to the need for a solid foundation in algebra and geometry before tackling more advanced topics like trigonometry.

Who May Find This Useful

This discussion may be useful for students learning about the concept of slope in mathematics, particularly those who are struggling with the foundational aspects of the topic or seeking clarification on related concepts.

  • #31
What I meant was that if you were to teach me math in the context of physics, I would better understand it.
 
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  • #32
If you have a line that has points on it but it is too hard to calculate rise over run because the results you have are obscure (for instance the line of best fit in an experiment), then this is a simple formula that I found on http://richardbowles.tripod.com:

[sum]X.[sum]Y - N.[sum]XY over ([sum]X)2 - N.[sum]X2
 
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  • #33
A day or so ago you hadn't any idea what a slope was and now you're asking about dy/dx? How about just taking it slowly and actually LEARNING each topic well before going on to the next?

(I notice that after not understanding the responses you got on this board, you complained that your teacher was "not good at explanations". I see a tendency to jump at ideas then complain about any explanation that does not verify your preconceptions.)

In any case, dy/dx has nothing to do with "infinite slopes". A straight line has a fixed slope (another way to calculate the slope it to take the tangent of the of the angle the line makes with any horizontal line). A curve does not have a "slope" but we can draw a tangent line to the curve and find its slope. That is dy/dx.
 

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