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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)