Relations

New Vocabulary:-

Coordinate system

Coordinate plane

x- and y- axes

Origin

Ordered pair

x- and y- Coordinates

relation

domain

range

independent variable

dependent vaiable

Why?

The deeper in the ocean you are, the greater pressure is on your body. This is because there is more water over you. The force of gravity pulls the water weight down, greater a greater pressure.
The equation that relates the total  pressure of the water to the depth is P=rgh, where
P = the pressure
r = the density of water,g = the acceleration due to gravity, andh = the height of water above you.
Represent a Relation This relationship between the depth and the pressure exerted can be represented by a line on a coordinate grid.
A coordinate system is formed by intersection of two number lines,the horizontal axis and the vertical axis.

A point is represented on a graph using order pairs.

• An order pair is a set of numbers,or coordinates, written in the form (x,y)

• The x- Value, called the x-coordinate, represents the horizontal placement of the point.

• The y- value, or y-coordinate, represents the vertical placement of the point.

A set of ordered pairs is called a relation. A relation can be depicted in several different ways. 

An equation can represent a relation as well as graphs, tables, and mappings.

A mapping illustrates how each elements of the domain is paired with an element in the domain is paired with an element in the range.
The set of the first numbers of the ordered pairs is the domain. The set of second numbers of the ordered pairs is the range  of the relation. This mapping represent the ordered pairs.

In a relation,
The value of the variable that determines the output is called the independent variable.
The variable with a value that is dependent on the value of the independent variable is called the dependent variable.
The domain contains values of the independent variable.
The range contains the values of the dependent variable.