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Subject: "Y-Intercept"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #249
Reading Topic #249
NJZ
Member since Mar-23-02
 Jul-16-03, 09:04 PM (EST)
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"Y-Intercept"
 
   Given two points in a plane, what is the most concise way to express the y-intercept associated with a linear relationship between the two points in terms of their coordinates? Any thoughts would be greatly appreciated. Thank you.

NJZ


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CSpeed0001
Member since Feb-19-03
 Jul-17-03, 12:24 PM (EST)
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1. "RE: Y-Intercept"
In response to message #0
 
   You mean like y=mx+b where m is the slope (found by finding the change in x over the change in y) and b is the y-intercept?

--CS


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NJZ
Member since Mar-23-02
 Jul-17-03, 03:07 PM (EST)
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2. "RE: Y-Intercept"
In response to message #1
 
   Yes, I'm looking for a simple way to express b in terms of the points (x1, y1) and (x2, y2) (sorry the subscripts don't work in this text). The slope m is (y2-y1)/(x2-x1), so you can write an equation for the line as (y-y1) = m(x-x1), or y = <(y2-y1)(x-x1)>/(x2-x1)+y1, or y = mx-mx1+y1, making b = y1-mx1. I was just wondering if there is a more concice way of expressing b.

NJZ


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Michael Klipper
guest
 Jul-17-03, 08:56 PM (EST)
 
3. "RE: Y-Intercept"
In response to message #2
 
   I very much doubt that there is any better formula.
Personally, I think the formula b = y1 - m*x1 is very nice. While it does require calculation of the slope, you can look at it as saying you start from y1 and you run down a hill of slope m over a distance of x1 horizontal units.


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Vladimir
Member since Jun-22-03
 Jul-18-03, 11:45 PM (EST)
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4. "RE: Y-Intercept"
In response to message #2
 
   If the two points A, B are on a line through the origin, we have a direct proportionality

yA/xA = yB/xB

and the y-axis intercept of this line is q = 0. If the 2 points are not colinear with the origin, i.e., we do not have a direct proportionality, the y-axis intercept tells us the distance we would have to shift the origin and the x-axis up/down to achive the direct proportionality:

(yA - q)/xA = (yB - q)/xB

However, I do not see it as a much of an improvement


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