MHB Why use point-slope form for linear equations?

AI Thread Summary
The discussion centers on the terminology and notation used in linear equations, specifically the slope-intercept form y = mx + b. The variable m represents the slope, while b denotes the y-intercept, although these symbols can vary by region, such as using k for slope in Russia. Participants express personal preferences for different variable names, like using s for slope instead of m. The point-slope form is also discussed, with the equation y - b = s(x - a) highlighted as a preferred format. Overall, the conversation emphasizes the flexibility in naming conventions within mathematical expressions.
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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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