Algebra Ch. 1 Definitions

The distance that a number is from zero on a number line

The opposite of a number. Additive inverses sum to zero

The mathematical phrase that can include numbers, variables, and operation symbols

A number that is multiplied repeatedly

Numerical factor when a term has a variable

A term that has no variable factor

A plane formed by two number lines that intersect at right angles

The numbers that make a ordered pair and identify the location of a point

Any example that proves a statement false

A process of reasoning, logically from given facts to a conclusion

An item in a matrix

Mathematical sentence that uses an equal sign

Substitute a given number for each variable and then simplify

A number that shows repeated multiplication

A mathematical sentence that compares the values of two expressions using an inequality symbol

Whole numbers and their opposites

A number that cannot be written as a ratio of two integers. Irrational numbers in decimal form is non-terminating and non-repeating

Terms with exactly the same variable factors in a variable expression

A rectangular arrangement of numbers. The number of rows and columns in the matrix determines its size

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

The counting numbers (-1, 0, 1, 2, 3...)

An equation that contains one or more variables

Two numbers that identify the location of a point

The point at which the axis of the coordinate plane intercept

The four parts into which the coordinate plane is divided by its axis

A real number that can be written as a ration of two integers. Rational numbers in decimal form are terminating or repeating

A number that is either rational or irrational

A graph that relates data of two different sets. The two sets of data are displayed as ordered pairs

Replace an expression with its simplest name of form

A number, variable, or the product or quotient of a number and one or more variables

A line on a scatter plot drawn near the points. It shows a correlation

A symbol, usually a letter, that represents one or more numbers

Nonnegative integers (0, 1, 2, 3...)

horizontal (x) and vertical (y) axis of the coordinate plane

location of an x-axis and y-axis of a point on the coordinate plane.

Integers that differ by one (-2, -1, 0, 1, 2…)

Equations that have the same solutions

Equation that is true for every value

Operations that undo one another

An equation involving two or more variables

Mean, median, and mode. They are used to organize/summarize a set of data

A data value that is much higher or lower than the other data values in the set

Any value(s) that make an equation true

A display of data made by using the digits of the values

The motion of an object moving at a constant rate

• Range = y
• Domain = x

Two inequalities that are joined by and/or

Equivalent inequalities have the same set of solutions

One variable – any value of values of a variable in the inequality that makes an inequality true

A number sequence formed by adding a fixed number to each previous term

The fixed number added to each term of an arithmetic sequence

Conclusion reached by inductive reasoning

Direct variation – nonzero constant k in the function y = kx

A variable that provides the output values of a function (y on the graph)

A linear function that can be expressed in the form y = kx, where k is not 0

A relation that assigns exactly one value in the range to each value of the domain

To write a rule in function notation, you use the symbol f(x) in place of y

An equation that describes a function

A variable that provides the imput values of a function (x in the graph)

Making conclusions based on observed patterns

Any set of ordered pairs

A number pattern

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

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

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

Equation whose graph forms a V that opens up or down

The most accurate trend line on a scatter plot showing the relationship between two sets of data

An equation whose graph forms a straight line

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

Two lines in the same plane that never intersect. Parallel lines have the same slope.

Lines that intersect to form right angles. 2 lines are perpendicular if the product of their slopes is -1

y-y₁ = m(x – x₁)

• Change in the dependent variable
• Change in the independent variable

• Ratio of the vertical change to horizontal change
• Vertical change = y₂ – y₁
• Horizontal change = x₂ – x₁
• Where x₂ – x₁ is not zero

A linear equation of a nonvertical line written as y = mx + b, where m = slope & b = y-intercept

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

A transformation that shifts a graph horizontally, vertically, or both

• 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
• Outputs - y

3 * r²