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Math Fornula

Innequality Properties

  1. If a < b, then a + c < b + c
  2. If a < b and c > 0, then ac < bc
  3. If a < b and c < 0, then ac > bc

Equations and Inequalities Involving Absolute Value

Definition:
|x| = x , if x > 0
|x| = -x , if x < 0
  1. |u| = a, for a > 0, if and only if u = -a, or u = a
  2. |u| < a, for a > 0 if and only if  -a < u < a
  3. |u| > a, for a > 0 if and only if u < -a or u > a

Cartesian Coordinates

Let P1 = (x1, y1) and P2 = (x2, y2) then

  1. The distance d between P1 and P2 is : d2 = (x2 - x1)2 + (y2 - y1)2
  2. The slope m is : m = (y2 - y1)/(x2 - x1)
  3. The slope intercept form of a line is : y = mx + b
  4. The point slope form of a line is : y - y1 = m(x - x1)