Find the equation of a line which passes through (6, 3) and (-3, -5).
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Step 1, find the slope, m.
m = diffy/diffx = (-5-3)/(-3-6) = 8/9
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Use y-y1 = m*(x-x1) where (x1,y1) is either point.
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Or,
| x y 1|
| 6 3 1| = 0
|-3 -5 1|
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x*(3*1 - -5*1) - y*(6*1 - (-3)*1) + 1*(6*(-5) - (-3)*3) = 0
8x -9y -21 = 0