# algebra formulas and definitions

whole numbers counting numbers and 0: 0, 1, 2, 3, …

integers positive whole numbers, their opposites, and zero: …, -3, -2, -1, 0, 1, 2, 3, …
rational numbers written as decimals, rational numbers terminate or repeat.
irrational numbers irrational numbers are numbers that cannot be writteen as fractions and dont terminate.
variable a letter or a symbol used to represent a value
constant a number or variable that doesnt change
minus, less than, diffrence
/ divided by, quotient
x times, product
absolute value a numbers distance from zero on a number line. it is indicated as |#|
opposites two numbers are opposites if their sum is zero. a number and its oppposite are the same distance from zero. They have the same absalute value.
additive inverse a number and its opposite.
+++ positive
-+- positive
++- negative
-++ negative
exponent tells how many times the base is used as a factor.
base is the number that is used as a factor.
perfect square is a number whose positive square root is a whole number.
natural numbers counting numbers
whole numbers are counting numbers and zero
integers whole numbers and their opposites
rational numbers can be expressed in the form a/b where a and b are both inetegrs and b
terminating decimals are rational numbers in decimal form that have a finite number of digits
Repeating decimals are rational numbers in decimal form that have a block of one or more digits that repeat continuisly.
P.E.M.D.A.S parentheses, exponents, multiply or divide, add or subtract
associative property when you are only adding or multiplying you can group any of the numbers together.
equation contains 2 variables can be used as a rule to generate ordered pairs.
ordered pair (x,y)
function notation y=f(x)
one-ste equation isolate the variable by inverse operations, you must do the same exact thing on the other side.
Two-step equation isolate the variable by inverse operations
when solving inequalities… multiply or divide by a negative #, flip!!!
linear function is a function whose graph forms a straight line.
y intercept where the graph intersects the y-axis.
x intercept where the graph intercets the x-axis
rate of change is a ratio that compares teh amount of change in a dependent variable to the amount of change in an independent variable.
rise is the difference in the y-value of two points on a line.
run is the diffrence in the x-value of two points on a line.
slope is the ratio of rise to run for any two points on the line.
positive slope line rises from left to right
negative slope line falls from left to right
zero slope horizontal line
undefined slope vertical line
Direct Variation is special type of linear relationship that can be written in the form y=kx, when k is a non-zero conctant called the constant of variation.
real numbers Real numbers include all rational and irrational numbers.