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# Math Fornula

**Innequality Properties**

- If a < b, then a + c < b + c
- If a < b and c > 0, then ac < bc
- 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

- |u| = a, for a > 0, if and only if u = -a, or u = a
- |u| < a, for a > 0 if and only if -a < u < a
- |u| > a, for a > 0 if and only if u < -a or u > a

**Cartesian Coordinates**

Let P_{1} = (x_{1}, y_{1}) and P_{2} = (x_{2}, y_{2}) then

- The distance d between P
_{1}and P_{2}is : d^{2}= (x_{2}- x_{1})^{2}+ (y_{2}- y_{1})^{2} - The slope m is : m = (y
_{2}- y_{1})/(x_{2}- x_{1}) - The slope intercept form of a line is : y = mx + b
- The point slope form of a line is : y - y
_{1}= m(x - x_{1})