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# Algebra

### algebra formulas and definitions

Question | Answer |
---|---|

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 |

+ | addition, more than, plus |

/ | 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. |

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