Algebra 1 Chapters 1-5 Vocabulary

Plotting a point

drawing the point on a number line that corresponds to a number. drawing on a coordinate plane that corresponds to the ordered pair

Entry,or element, of a matrix

each number in a matrix

equivalent equations

equations with the same solutions as the original equation

Solving the equation

finding all the solutions of an equation

reciprocal

flipped fraction

negative correlation

negative

quadrants

on of four parts into which the axes divide a coordinate plane

inverse operations

operations that undo each other, such as addition and subtraction

positive correlation

positive

Grouping symbols

symbols such as parentheses or brackets that indicate the order in which operations should be performed.

like terms

terms that have the same variable raised to the same power

constant terms

terms with no factors

Domain

the collection of all input values

Range

the collection of all the output values

constant variation

the constant in a variation model, represented by the letter k

outcomes

the different possible results of a probability experiment

point-slope form

the equation of a nonvertical line y-y1= m(x-x1) that passes through a given point (x1,y1) with a slope of m

x- coordinate

the first number in an ordered pair

x- axis

the horizontal axis in a coordinate plane

slope

the number of units a non vertical line rises or falls for each unit of horizontal change from left to right, the slope is m

Exponent

the number or variable that represents the number of times the base is used as a factor

Values

the numbers represented by variables

favorable outcomes

the outcomes for a particular event that are being considered

Terms of an expression

the parts that are added in an expression. 5-t terms are 5 and -t

origin

the point (0,0) in a coordinate plane at which the horizontal axis intersects the vertical axis

graph of an ordered pair

the point in the plane that corresponds to an ordered pair

Origin

the point labeled zero on the number line

Graph of a number

the point that corresponds to a number

Distributive property

the product of a and (b+c)

odds

the ratio of the number of ways an event can occur to the number of ways the event cannot occur

rate of a per b

the relationship a/b of two quantities a and b that are measured in different units

ratio of a to b

the relationship a/b of two quantities a and b that are measured in the same unit

direct variation

the relationship of two variables x and y if there is a nonzero number k such that y=kx or y/x = k the x and y vary directly

solution step

the result of applying a transformation to an equation when solving the equation

properties of equality

the rules of algebra used to transform equations in equivalent equations

y- coordinate

the second number in an ordered pair

graph of an equation in two variables

the set of all points (x,y) that are solutions of the equation

y- axis

the vertical axis in a coordinate plane

x- intercept

the x-coordinate of a point where a graph crosses the x- axis

y- intercept

the y-coordinate of a point where a graph crosses the y- axis

Evaluating the expression

to find the value of an expression by replacing each variable by a number

parallel lines

two different lines in the same plane that do not intercept

Opposites

two points on a number line that are the same distance from the origin but are on opposite sides of it

similar triangles

two triangles are similar if they have equal corresponding angles. it can be shown that this is equivalent to the ratios of the lengths of the corresponding sides being equal

Input

x values

Output

y values

Absolute Value

distance between the origin and the point representing the real number. | a |

Bar graph

A graph that organizes a collection of data by using horizontal or vertical bars to display how many times each event or number occurs in the collection

Line graph

A graph that uses line segments to connect data points. Shows changes over time

Real number line

A line that pictures real numbers as points

Solution of an inequality

A number that, when substituted for the variable in an equation results in a true statement

Solution of an inequality

A number that, when substituted for the variable in an equation, results in a true statement

Function

A rule that establishes a relationship between two quantities, called the input output. for each input there is exactly one output.

Inequality

A sentence formed when an inequality symbol is placed between two expressions

Equation

A statement formed when an equal sign is placed between two expressions

Input-output table

A table used to describe a function by listing the inputs and the outputs

linear equation in one variable

An equation in which the variable is raised to the first power and does not occur in a denominator, inside a square root symbol, or inside an absolute value symbol

Open sentence

An equation that contains one or more vaiables

Verbal model

An expression that uses words to represent a real-life situation

Mathematical model

An expression,equation,or inequality that represents a real-life situation

theoretical probability

a type of probability that is based on the numbers of favorable outcomes divided by the total number of outcomes

function notation

a way to name a function that is defined by an equation. for an equation x and y the symbol f (x) replaces y and is read as " the value of f at x" or simply as " f of x"

formula

an algebraic equation that relates two or more real-life quantities

identity

an equation that that is true for all values of the variables

Counter examples

an example used to show that a given statement is false

simplified expressions

an expression is simplified if it has no symbols of grouping and if all the like terms have been combined

solution of a linear equation

an ordered pair is a solution of a linear equation if the equation is true when the values of x and y are substituted into the equation

Positive numbers

any of the numbers greater than zero

Data

Information,facts, or numbers used to describe something

Negative numbers

any of the numbers less than zero

Integers

any of the whole numbers -1,0,1,2

relation

any set of ordered pairs

Variable expression

collection or numbers, variables, and operations

Unit analysis

Writing the units of each variable in a real-life problem to help determine the units for the answer

linear interpolation

a method of estimating the coordinates of a point that lies between two given data points

linear extrapolation

a method of estimating the coordinates of a point that lies to the right or left of all the given data points

coefficient

a number multiplied by a variable in a term the number is the coefficient of the variable.

ordered pair

a pair of numbers used to identify a point in a plane

coordinate plane

a plane formed by two real number lines that intersect at a right angle

experimental probability

a probability that is based on repetitions of an actual experiment

round-off error

The error produced when a decimal result is rounded in order to provide a meaningful answer

Base

The number or variable that is used as a factor in repeating multiplication

Power

The result of repeated multiplication

Order of operations

The rules established to evaluate an expression involving more than one operation

graph of a function

The set of all points (x,f(x)) where x is the domain of the function

Real numbers

The set of numbers consisting of the positive numbers, the negative numbers and zero

Velocity

The speed and direction in which an object is traveling. the speed of an object is its absolute value

unit rate

a rate per one given unit

Matrix

a rectangular arrangement of numbers into horizontal rows and vertical columns

Modeling

Writing algebraic expressions,equations,or inequalities that represent real-life situations

rate of change

a comparison of two different quantities that are changing. slope provides an important way of visualizing a rate of change

scatter plot

a graph of pairs of numbers that represent real life situations. it is a way to analyze the relationship between two quantities

Variable

a letter that is used to represent one or more numbers

best-fitting line

a line that best fits the data points on a scatter plot

standard form

a linear equation of the form Ax+ By=C where A,B, and C are real numbers and A and B are not both zero

slope- intercept form

a linear equation written in the form y=mx+b . the slope of the line is m the y intercept is b

probability of an event

a measure of the likelihood that the event will occur due to chance. it is a number between 0 and 1, inclusive