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Algebra Vocab: U. 4

Vocabulary List for Math Class Unit Four

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)
Created by: Amo.Alexa.1920