Line Equations: Rearranging Ax + By + C = 0 to y=mx+b

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Discussion Overview

The discussion revolves around the rearrangement of the general line equation Ax + By + C = 0 into the slope-intercept form y = mx + b. Participants explore methods for this transformation and consider special cases, such as vertical lines.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires whether it is possible to rearrange the general line equation into slope-intercept form.
  • Another participant asks about the methods others have used for this rearrangement.
  • A participant describes their attempt to isolate y, resulting in the expression Y = (-a/-b)x + (-c/-b), expressing uncertainty about its correctness.
  • It is noted that simplification of the expression is possible, but that the rearrangement does not hold if B = 0.
  • A participant mentions that vertical lines represent special cases of the general equation and cannot be expressed in slope-intercept form due to an undefined slope.

Areas of Agreement / Disagreement

Participants express differing views on the rearrangement process and the implications for vertical lines, indicating that the discussion remains unresolved regarding the correctness of specific methods and the treatment of special cases.

Contextual Notes

There are limitations regarding the assumptions made about the values of A, B, and C, particularly concerning the case when B = 0, which affects the ability to rearrange the equation.

Einstein's Cat
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Say a line equation is expressed with the General equation of Ax + By + C = 0; can one just simply rearrage this into the form of y= mx + b?
 
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What ways of rearranging Ax + By + C = 0 into the form y= mx + b have you tried ?
 
Nidum said:
What ways of rearranging Ax + By + C = 0 into the form y= mx + b have you tried ?
I just made y the subject so that
Y= (-a/-b)x + (-c/-b); this may not be correct, I've just done it now
 
You can simplify the expression.
It doesn't work if b=0.

You can always perform all allowed operations on equations.
 
Einstein's Cat said:
Say a line equation is expressed with the General equation of Ax + By + C = 0; can one just simply rearrage this into the form of y= mx + b?
Vertical lines such as x = 2 are special cases of the general equation (A = 1, B = 0, C = -2), but can't be written in the slope-intercept form, since the slope is undefined. Any other line that isn't vertical can be written in either equation form.
 

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