# Algebra Ch. 1 Definitions

 Absolute value The distance that a number is from zero on a number line Additive inverse The opposite of a number. Additive inverses sum to zero Algebraic expression The mathematical phrase that can include numbers, variables, and operation symbols Base A number that is multiplied repeatedly Coefficient Numerical factor when a term has a variable Constant A term that has no variable factor Coordinate plane A plane formed by two number lines that intersect at right angles Coordinates The numbers that make a ordered pair and identify the location of a point Counterexample Any example that proves a statement false Deductive reasoning A process of reasoning, logically from given facts to a conclusion Element An item in a matrix Equation Mathematical sentence that uses an equal sign Evaluate Substitute a given number for each variable and then simplify Exponent A number that shows repeated multiplication Inequality A mathematical sentence that compares the values of two expressions using an inequality symbol Integers Whole numbers and their opposites Irrational numbers A number that cannot be written as a ratio of two integers. Irrational numbers in decimal form is non-terminating and non-repeating Like terms Terms with exactly the same variable factors in a variable expression Matrix A rectangular arrangement of numbers. The number of rows and columns in the matrix determines its size Multiplicative inverse/reciprocal Given a nonzero rational number, a/b, the multiplicative inverse, or reciprocal, is b/a. The product of a nonzero number and its multiplicative inverse is always one Natural numbers The counting numbers (-1, 0, 1, 2, 3...) Open sentence An equation that contains one or more variables Ordered pair Two numbers that identify the location of a point Origin The point at which the axis of the coordinate plane intercept Quadrants The four parts into which the coordinate plane is divided by its axis Rational numbers A real number that can be written as a ration of two integers. Rational numbers in decimal form are terminating or repeating Real numbers A number that is either rational or irrational Scatter plot A graph that relates data of two different sets. The two sets of data are displayed as ordered pairs Simplify Replace an expression with its simplest name of form Term A number, variable, or the product or quotient of a number and one or more variables Trend line A line on a scatter plot drawn near the points. It shows a correlation Variable A symbol, usually a letter, that represents one or more numbers Whole numbers Nonnegative integers (0, 1, 2, 3...) x-axis and y-axis horizontal (x) and vertical (y) axis of the coordinate plane x-coordinate and y-coordinate location of an x-axis and y-axis of a point on the coordinate plane. Consecutive integers Integers that differ by one (-2, -1, 0, 1, 2…) Equivalent equations Equations that have the same solutions Identity Equation that is true for every value Inverse operations Operations that undo one another Literal equation An equation involving two or more variables Measures of central tendency Mean, median, and mode. They are used to organize/summarize a set of data Outlier A data value that is much higher or lower than the other data values in the set Solution of an equation Any value(s) that make an equation true Stem-and-leaf plot A display of data made by using the digits of the values Uniform motion The motion of an object moving at a constant rate Range = x or y? Domain = x or y? Range = yDomain = x Compound inequalities Two inequalities that are joined by and/or Equivalent inequalities Equivalent inequalities have the same set of solutions Solution of an inequality One variable – any value of values of a variable in the inequality that makes an inequality true Arithmetic sequence A number sequence formed by adding a fixed number to each previous term Common difference The fixed number added to each term of an arithmetic sequence Conjecture Conclusion reached by inductive reasoning Constant of variation Direct variation – nonzero constant k in the function y = kx Dependent variable A variable that provides the output values of a function (y on the graph) Direct variation A linear function that can be expressed in the form y = kx, where k is not 0 Function A relation that assigns exactly one value in the range to each value of the domain Function notation To write a rule in function notation, you use the symbol f(x) in place of y Function rule An equation that describes a function Independent variable A variable that provides the imput values of a function (x in the graph) Inductive reasoning Making conclusions based on observed patterns Relation Any set of ordered pairs Sequence A number pattern Term A number, variable, or the product or quotient of a number and one of more variables Ex: 5x + (y/2) – 8 has three terms – 5x, y/2, -8 Vertical-line test A method used to determine if a relation is a function or not. If the line passes through a graph more than once, the graph is NOT a function Correlation Coefficient A number that tells how closely the equation of best fit models the data. The value r of the correlation coefficient is in the range -1 < r < 1 Absolute value equation Equation whose graph forms a V that opens up or down Line of best fit The most accurate trend line on a scatter plot showing the relationship between two sets of data Linear equation An equation whose graph forms a straight line Negative reciprocal A number of the form –b/a, where a/b is a nonzero rational number. The product of a number and its negative reciprocal is -1 Parallel lines Two lines in the same plane that never intersect. Parallel lines have the same slope. Perpendicular lines Lines that intersect to form right angles. 2 lines are perpendicular if the product of their slopes is -1 Point-slope form y-y₁ = m(x – x₁) Rate of change Change in the dependent variable Change in the independent variable Slope Ratio of the vertical change to horizontal change Vertical change = y₂ – y₁ Horizontal change = x₂ – x₁ Where x₂ – x₁ is not zero Slope-intercept form A linear equation of a nonvertical line written as y = mx + b, where m = slope & b = y-intercept Standard form of a linear equation The form of a linear equation Ax + By = C, where A, B, and C are real numbers and A and B are not zero Translation A transformation that shifts a graph horizontally, vertically, or both x-intercept/y-intercept x-coordinate of the point where a line crosses the x-axis y-coordinate of the point where a line crosses the y-axis Inputs - x or y? Outputs - x or y? Inputs - xOutputs - y How to solve 3r2? 3 * r2 AuthorThorby ID56008 Card SetAlgebra Ch. 1 Definitions DescriptionChapter one Vocab Updated2010-12-15T01:43:41Z Show Answers