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Kustaz

Converting 1(X,Y) & 2(X,Y) to Y = Mx + C

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how would I convert a vector, supplied in the format of two coordinates, into the linear equation form (Y = Mx + C)? PS: Explanation of the conversion process would be much appreciated.

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You have two points so that means you can get the slope.

Once you have the slope then To find the intersect. plug one point into the standard equation and solve for C.

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Vectors A = {x1,y1} and B = {x2,y2}
__
Line AB in Cartesian format:

Gradient of a line is rise over run:

M = y2 - y1
-------
x2 - x1

Intercept is found by finding the vertical shift required to align the line with the vectors

y = M*x + c
=> c = y - M*x
=> c = y1 - M*x1 (or c = y2 - M*x2)

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M is the slope, given by the equation: m=(y2-y1)/(x2-x1).
After finding M, just get one of the two points' above mentioned coordinates and place them in the appropriate places in the equation, and solve for C (for example, if you took the point (x1,y1) - you'd do C=y1-mx1).
after this, just rebuild your equation using M and C you've just found.
Practical example:
assuming we got two points A(2,3) and B(4,5).
We'll first find the slope (M): m=(y2-y1)/(x2-x1)=(5-3)/(4-2)=2/2=1.
Now, we'll find C (I'll use point A coordinate's here): C=y1-mx1=3-1*2=3-2=1.
Now we'll rebuild our equation using M and C: y=x+1.
Have fun :] if anything isn't clear, feel free to ask...!

EDIT: had some calculation mistakes, but it's all fixed now...

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