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Linear Functions


function a relation where each item of the domain is paired with exactly one item in the range
independent variable all values in the domain; x-values; these items are chosen
dependent variable all values in the range; y-values; these will depend on the domain
vertical line test when looking at a graph, a vertical line passes through no more than one point on the graph; if it passes through more than one point, it is not a function
function rule describes the operations performed on the domain to get the range; written in equation form... y = 2x + 3
function notation a way to write an equation; f(x) = 2x + 3 where f(x) is basically the same as "y"
proportional relationship has a constant of proportionality; graphs a straight line; line passes through the origin
linear equation an equation whose line is a graph
linear function a function in which the graph of the solutions form a straight line
function table a table that shows the values for x, y, and the rule
x-intercept point where the graph crosses the x-axis (y = zero)
y-intercept point where the graph crosses the y-axis (x = zero); identified by the variable "b" in the slope-intercept form
rate of change rate that describes how one quantity changes in relation to another quantity (positive = increase; negative = decrease; zero = no change)
linear relationship where the rate of change between any two quantities is the same
constant rate of change the same change between any two quantities (unit rate)
slope ratio of the vertical change to the horizontal change (steepness of the line); m = (y2 - y1) / (x2 - x1); slope can be positive, negative, no slope, or undefined
slope-intercept form y = mx + b where "m" is the slope and "b" is the y-intercept
system of equations a collection of two or more equations with the same set of varibables
substitution using Algebraic methods to find the exact solution of a system of equations