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Linear Equations (General and Standard forms: From Wikipedia) 
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#1
Feb1112, 07:52 AM

P: 26

Source: http://en.wikipedia.org/wiki/Linear_equation
General form: It says (under the title General Form) "If B is nonzero, then the yintercept, that is the ycoordinate of the point where the graph crosses the yaxis (where x is zero), is −C/B, and the slope of the line is −A/B." How is the slope deduced to be A/B? Standard form: Aren't this form contradictory to the first form? I mean, both are the same, but here C is positive, and on the left side of the equation, while in the General Form, C is positive, and on the right side of the equation. 


#2
Feb1112, 09:55 AM

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P: 6,189

If x increases by 1, Ax increases by A, so By has to decrease by A. More specifically if y changes by A/B, then By changes by A. The second form is a new equation in which the old A, B and C no longer apply. It is more or less related to the first form, but as you already surmised the C in the second form would have to be minus the C of the first form, if A and B are the same. 


#3
Feb1112, 11:32 AM

P: 26

But I thought the change doesn't have to be 1 in x? What if the change is p?



#4
Feb1112, 11:33 AM

HW Helper
P: 6,189

Linear Equations (General and Standard forms: From Wikipedia)
If x changes by p, then y will change by p times the slope. 


#5
Feb1112, 11:42 AM

P: 26

From Wikipedia: "The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line. "
That's what I meant. "The slope of a line is the amount that y changes if x increases by 1. If x increases by 1, Ax increases by A, so By has to decrease by A." So, if x increases by p, Ax increase by Ap, so By has to decrease by Ap. (So, y = Ap/B). This means Ap/B should be the slope in general for the equation Ax + By + C = 0. Or is my conclusion wrong? 


#6
Feb1112, 11:44 AM

HW Helper
P: 6,189

As you say, the slope is the change in the y coordinate divided by the corresponding change in the x coordinate.
Since Ap/B is the change in y if x changes by p, that means that the slope is Ap/B divided by p, which is A/B. 


#7
Feb1112, 11:47 AM

P: 26

That's right.
Thank you :) 


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