Learning about finding the slope of a line

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SUMMARY

This discussion centers on understanding the concept of slope in mathematics, specifically in the context of pre-algebra. The slope of a line is defined as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run), expressed mathematically as m = dy/dx. Participants clarify that the slope remains constant regardless of the two points chosen on the line, and they emphasize the importance of mastering foundational concepts such as algebra and geometry before progressing to trigonometry and calculus. The discussion also highlights the significance of using clear notation and understanding the relationship between slope and angles.

PREREQUISITES
  • Understanding of basic algebraic concepts
  • Familiarity with coordinate systems and graphing
  • Knowledge of rise and run terminology
  • Basic comprehension of functions and their properties
NEXT STEPS
  • Study the concept of slope in greater detail, focusing on the formula m = (y2 - y1) / (x2 - x1)
  • Learn about graphing linear equations and interpreting their slopes
  • Explore the relationship between slope and angles using trigonometric functions
  • Investigate the progression from algebra to geometry, and then to trigonometry and calculus
USEFUL FOR

Students in pre-algebra, educators teaching foundational math concepts, and anyone seeking to strengthen their understanding of linear relationships and slope calculations.

  • #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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