Algebra 2 Chapter 4 Flashcards

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.