Understanding the Concept of "y=mx+b

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The discussion centers on understanding the equation y = mx + b, which represents a linear relationship where m is the slope (or steepness) of the line and b is the y-intercept, indicating where the line crosses the y-axis. Participants explain that the equation defines a straight line, with variations leading to different shapes like parabolas when additional terms are included. The reasoning behind the equation is that it captures the relationship between x and y in a linear form, where any straight line can be expressed as such. Additionally, the conversation touches on solving systems of equations and the implications of different outcomes, such as "no solution" or "infinite solutions," which relate to the slopes and y-intercepts of the lines involved. Overall, the thread emphasizes the foundational concepts of linear equations and their graphical interpretations.
  • #51
2's the right answer, whether by elimination or thinking it out, nobody cares? ;)

For reference, a vertical or horizontal line will be in only two quadrants. For example, if m = 0 and b = 1, we have the line

y = 1

which is only in the first and second quadrants.

Stem cell research, eh? I guess I can have a look...

cookiemonster
 
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  • #52
I noticed that this thread has changed subject a couple times. There is no hard policy on this, but information will later be easier to find if we use new threads for new subjects.

My point is that, if you have some other, new question, feel free to open a new thread (unless, of course, it is closely related to this one).
 
  • #53
cookiemonster said:
For reference, a vertical or horizontal line will be in only two quadrants.

cookiemonster

But you never said a vertical/horizontal line; you said non-vertical and non horizontal. Lines can be diagonal too. But I guess it was my folly here; I didn't ask specifically.

thanks so much!

Sorry about that arhkron.
 
  • #54
Ah, sorry. I remember saying not to consider vertical lines because the equation to describe them doesn't work like you normally expect y = mx + b to.

Anyway, I mean that only vertical or horizontal lines will be in two quadrants. If a line is diagonal in the slightest, it will end up in three quadrants. Except for maybe lines that pass through the origin...

cookiemonster
 
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