Lesson Intermediate Algebra Formulas Review

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This Lesson (Intermediate Algebra Formulas Review) was created by by sofiyacherni(96) About Me : View Source, Show
About sofiyacherni: B.S. in Math from South Dakota School of Mines and Technology
ALGEBRAIC PROPERTIES
Commutative Property:
a + b = b + a(for addition)
ab = ba (for multiplication)
Associative Property:
(a + b) + c = a + (b + c)(for addition)
(ab)*c = a*(bc)(for multiplication)
Distributive Property of Multiplication Over Addition:
a*(b + c) = ab + ac
(b + c)*a = ba + ca
Identity Property:
a + 0 = a(for addition)
a*1 = a(for multiplication)

PROPERTIES OF EXPONENTS
Product of Powers
a^m*a^n=a^(m+n)
Power of Power
(a^m)^n=a^(mn)
Power of a Product
(ab)^m=a^m*b^m
Negative Exponent
a^(-m)=1/(a^m) where a<>0
Zero Exponent
a^0=1 where a<>0
Quotient of Powers
(a^m)/(a^n)=a^(m-n) where a<>0
Powers of a Quotient
(a/b)^m=(a^m)/(b^m) where b<>0

SLOPES AND INTERCEPTS
If a line passes through points (x1,y1) and (x2,y2) the the slope m is
m=(y2-y1)/(x2-x1)
If a line passes through a point (x1,y1) with a slope m then the equation for that line is
y-y1=m(x-x1) (point-slope form)
If an equation for a line is in a slope-intercept form
y=mx+b then the ordered pair (0,b) is the y-intercept
If an equation for a line is in the form
x=(1/m)y+c then the ordered pair (c,0) is the x-intercept

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