Algebra 2 Chapter 4 Flashcards

Questions and Answers

What is an ordered pair?

A pair of numbers written in brackets with no specific order

A pair of numbers written in parentheses where order is important (correct)

A single number written in multiple forms

A pair of numbers displayed in a table

When two number lines intersect at a right angle, the ___ is the common 0 point.

origin

What is the x-axis?

The horizontal number line in a rectangular coordinate system.

What is the y-axis?

The vertical number line in a rectangular coordinate system. Signup and view all the answers

Two number lines that intersect at a right angle at their 0 points form a ______.

rectangular (Cartesian) coordinate system Signup and view all the answers

What does it mean to plot an ordered pair?

To locate it on a rectangular coordinate system. Signup and view all the answers

The two numbers in an ordered pair are the _____ of the ordered pair.

components Signup and view all the answers

Each number in an ordered pair represents a ____ of the corresponding point.

coordinate Signup and view all the answers

What is a quadrant?

One of the four regions in the plane determined by a rectangular coordinate system. Signup and view all the answers

What is the graph of an equation?

The set of points corresponding to all ordered pairs that satisfy the equation. Signup and view all the answers

What is a first-degree equation?

An equation that has no term with a variable to a power greater than one. Signup and view all the answers

What is a linear equation in two variables?

A first-degree equation with two variables. Signup and view all the answers

What is the x-intercept?

The point where a line intersects the x-axis. Signup and view all the answers

What is the y-intercept?

The point where a line intersects the y-axis. Signup and view all the answers

What is rise in the context of a line?

The vertical change between two points. Signup and view all the answers

What is run in the context of a line?

The horizontal change between two points on the line. Signup and view all the answers

What is slope?

The ratio of the change in y compared to the change in x along a line. Signup and view all the answers

What are linear inequalities in two variables?

A first-degree inequality with two variables. Signup and view all the answers

In the graph of a linear inequality, the _____ separates the regions that satisfy and do not satisfy the inequality.

boundary line Signup and view all the answers

If the quantity y depends on x, then y is called the _____ in a relation between x and y.

dependent variable Signup and view all the answers

If y depends on x then x is the ____ in a relation between x and y.

independent variable Signup and view all the answers

What is a relation?

A set of ordered pairs of real numbers. Signup and view all the answers

What is a function?

A set of ordered pairs in which each value of the first component, x, corresponds to exactly one value of the second component, y. Signup and view all the answers

What is the domain of a relation?

The set of first components (x-values) of the ordered pairs of the relation. Signup and view all the answers

What is the range of a relation?

The set of second components (y-values) of the ordered pairs of the relation. Signup and view all the answers

What is function notation?

Another way to represent the dependent variable y for the function f. Signup and view all the answers

What is a linear function?

That is defined by f(x) = mx + b. Signup and view all the answers

What is a constant function?

A linear function of the form f(x) = b, for a real number b. Signup and view all the answers

Study Notes

Ordered Pairs and Coordinate System

An ordered pair consists of two numbers in parentheses, where the sequence matters significantly.
The origin of a rectangular coordinate system is situated at the intersecting point of the two axes, noted as (0,0).
The x-axis represents the horizontal line on a coordinate plane, while the y-axis represents the vertical line.

Rectangular Coordinate System

A rectangular (Cartesian) coordinate system comprises two intersecting number lines at right angles, defining a plane.
Plotting involves locating an ordered pair on the rectangular coordinate system.

Components and Coordinates

Each ordered pair has components, which are the individual numbers that comprise it.
A number in an ordered pair signifies a coordinate of a point in the coordinate plane.

Quadrants and Graphs

The coordinate plane is divided into quadrants, totaling four regions based on the positive and negative values of x and y.
The graph of an equation can be visualized as a set of points that satisfy the equation.

Linear Equations

A first-degree equation includes no variables raised to a power higher than one.
A linear equation in two variables is defined by its first-degree nature with two different variables, typically expressed in the form Ax + By = C.

Intercepts and Changes

The x-intercept is where a line crosses the x-axis, while the y-intercept is where it intersects the y-axis.
The rise indicates the vertical change between two points, whereas the run indicates the horizontal change.

Slope and Inequalities

The slope of a line measures the ratio of rise to run, representing how steep the line is.
Linear inequalities in two variables express a relationship comparable to a linear equation but involve inequality signs.

Boundary Lines and Variables

In linear inequalities, a boundary line differentiates between regions that satisfy the inequality and those that do not.
Dependent variable refers to y, which relies on x, while x is labeled as the independent variable.

Relations and Functions

A relation consists of a set of ordered pairs of real numbers.
A function is a specific relation where each x value corresponds to one unique y value.

Domain and Range

The domain of a relation includes all first components (x-values), while the range consists of second components (y-values).

Function Notation and Types

Function notation offers an alternative method to express the dependent variable y as f(x).
A linear function is specifically characterized by the formula f(x) = mx + b, where m is the slope and b is the y-intercept.
A constant function is a type of linear function represented solely as f(x) = b, indicating that it does not change irrespective of x.

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Test your understanding of key concepts in Algebra 2 with these flashcards from Chapter 4. Each card provides essential definitions and terms that are fundamental to grasping the subject matter. Perfect for quick revision and self-assessment.