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# Algebra Vocab: U. 4

### Vocabulary List for Math Class Unit Four

Term | Definition |
---|---|

proportional relationships | two variables with respective values are always in the same ratio (they have the same relative size to one another). One variable is always a constant multiple of other. In equation form if the two variables are x and y: y/x = k or kx = y |

constant of proportionality | if one variable is always the product of the other and a constant, the two are directly proportional. x and y are directly proportional if the ratio yx is constant. In y/x = k and kx = y k is the constant of proportionality |

conversions | feet in a mile, inches in a foot, feet in a yard, minutes in an hour, months in a year, cm in a meter, meters in a km, minutes in an hour, quarts in a gallon, pints in a quart, cups in a pint |

the slope-intercept form of a linear function | given a linear equation, f(x), it can be expressed in equation form by: f(x) = y = mx + b. m = average rate of change = slope = delta y/ delta x and b = y-intercept of the line |

non-proportional linear relationsips | form a line when graphed; if two points in a line are not equal, it is not proportional; variables are not constant multiples of the other |

negative slope | moves upward on a graph from left to right |

positive slope | moves downward on a graph from left to right |

critical linear model facts: slope and y-intercept | all linear models in the form y = mx +b have two parameters, the slope, m, and the y-intercept, b: 1. The slope, m, tells us how fast the output is changing relative to the input 2. The y-intercept, b, always tells us the output's starting value ( x = 0) |

horizontal line | y = constant (constants can be determined by using any point the line passes through) |

vertical line | x = constant (constants can be determined by using any point the line passes through) |

absolute value function | a function that contains an algebraic expression within absolute value symbols which gives us the "size" or magnitude of a number. The absolute value of a number is its distance from 0 on the number line |

step function | a function that has outputs to a particular function that are constant over particular ranges |

graphing equations and inequalities | the connection between graph and equations/inequalities: 1. Any coordinate pair(x, y) that makes an equation or inequality true lies on the graph 2. The entire graph is a collection of all the (x, y) pairs that make the equation or inequality true |

sequence | a function whose set of inputs, the domain, is a subset of the natural numbers, i.e. {1, 2, 3, 4...} . It is often shown as an ordered list of numbers, called the terms or elements of the sequence |

arithmetic sequences | sequences where the terms in the list increase or decrease by the same amount given a unit increase in the index (where the number is in line) |