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

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SUMMARY

The discussion focuses on rearranging the general line equation Ax + By + C = 0 into the slope-intercept form y = mx + b. Participants confirmed that the rearrangement is valid for non-vertical lines, where the slope (m) can be expressed as -A/B and the y-intercept (b) as -C/B. It was noted that vertical lines, such as x = 2, cannot be expressed in slope-intercept form due to an undefined slope when B equals zero. Simplifying the expression is also possible, provided the conditions are met.

PREREQUISITES
  • Understanding of linear equations and their standard forms
  • Familiarity with algebraic manipulation techniques
  • Knowledge of slope-intercept form of a line
  • Concept of undefined slope in vertical lines
NEXT STEPS
  • Practice rearranging various linear equations into slope-intercept form
  • Explore the implications of vertical lines in coordinate geometry
  • Learn about the significance of slope (m) and y-intercept (b) in graphing
  • Investigate special cases in linear equations, such as parallel and perpendicular lines
USEFUL FOR

Students learning algebra, educators teaching linear equations, and anyone interested in mastering the manipulation of line equations for graphing and analysis.

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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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