Why use point-slope form for linear equations?

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Discussion Overview

The discussion revolves around the naming conventions and preferences for representing linear equations, specifically focusing on the slope-intercept form and point-slope form. Participants explore the rationale behind the variables used for slope and y-intercept, as well as personal preferences for notation.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants inquire about the reasons behind the naming of the slope-intercept form as y = mx + b.
  • One participant notes that while $m$ is commonly used for slope, in some regions like Russia, $k$ is preferred, although $b$ for the y-intercept remains consistent.
  • Another participant expresses a preference for using $s$ as the variable for slope, suggesting alternatives like y = sx + b or f(x) = sx + b.
  • A participant reiterates their preference for $s$ for slope, indicating agreement with the alternative notation.
  • One participant proposes the point-slope form as y - b = s(x - a), identifying $a$ and $b$ as coordinates of a specific point.

Areas of Agreement / Disagreement

Participants express differing preferences for variable names in linear equations, indicating a lack of consensus on the best notation. The discussion remains open with multiple viewpoints on the subject.

Contextual Notes

Participants mention variations in notation across different cultures, highlighting the dependence on regional conventions. No specific assumptions or limitations are resolved.

mathdad
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Why is y = mx + b called the slope-intercept form?

Why is m the chosen variable for slope?

Why is b the chosen variable representing the y-intercept?
 
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RTCNTC said:
Why is y = mx + b called the slope-intercept form?
Because $m$ is the slope and $b$ is the $y$-intercept.

RTCNTC said:
Why is m the chosen variable for slope?

Why is b the chosen variable representing the y-intercept?
If you mean the variable names $m$ and $b$, they are such only in some circles. In Russia, for example, it is customary to denote the slope by $k$, though the intercept is still often denoted by $b$. You are free to call than any names, such as $y=\xi x+\aleph$.
 
I like s for slope. I guess b is ok for the y-intercept.

I like it this way: y = sx + b or f(x) = sx + b.
 
RTCNTC said:
I like s for slope.
This makes sense.
 
For the point-slope, I like y - b = s(x - a), where a and b are the coordinates of the point (a, b).
 

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