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Home Q & A Board Science-Related Homework Help Mathematics
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toni85 toni85
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10 years ago
I was doing some calculus homework and I am embarrassed to say that I got confused with how to turn Point-Slope Form into the General Equation of a Line. (It's been a while) I've got two textbooks here, one of them is Calculus: A First Course by James Stewart, and a few other authors, and Precalculus: Fifth Edition which is also by James Stewart as well as some other authors. The first book gives the example y - 3 = 4 (x - 1) ---> y - 3 = 4x - 4 ---> 4x - y - 1 = 0. This is the way I thought it was always done, by bringing the y-term and the constant to the other side of the x-term. But then the second book has the example: y + 3 = -1/2 (x - 1) ---> 2y + 6 = -x + 1 ---> x + 2y + 5 = 0. Here they bring x-term and constant +1 to the other side of the equation. I noticed they use this formula through out the chapter. Which is correct?
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#1
10 years ago
ummm.. both are correct.  Neither way is ''wrong'' - they are actually doing exactly the same thing, for all practical purposes.  The main difference is just in how you want to view the re-arranging going on.  In the general methodology, when you are done, the multiplier of 'x' is positive - though this is not an absolute requirment.
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#2
10 years ago
GASPP how embarrassing
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#3
10 years ago
The first book gives the example y - 3 = 4 (x - 1) ---> y - 3 = 4x - 4 ---> 4x - y - 1 = 0. This is the way I thought it was always done, by bringing the y-term and the constant to the other side of the x-term. But then the second book has the example: y + 3 = -1/2 (x - 1) ---> 2y + 6 = -x + 1 ---> x + 2y + 5 = 0.
No contradictions.  Look here:
y - 3 = 4 (x - 1)  gives y - 3 = 4x - 4, subtract (y-3) both sides get 0 =  4x - 4 - y + 3, hence 4x - y - 1 = 0.

Similarly, y + 3 = -1/2 (x - 1), x 2 both sides gives  2y + 6 = -x + 1, and subtract (-x+1) both sides, we have  x + 2y + 5 = 0.
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mheikellmheikell
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10 years ago
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